[{"data":1,"prerenderedAt":4327},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz":4317},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":441,"checks":4255,"conditions":4273,"conditionsHtml":4274,"deprecated":4275,"description":4249,"extension":4276,"figure":4275,"figureCaption":4275,"figureHtml":4275,"formulaId":4277,"latex":4278,"latexHtml":4279,"level":4280,"meta":4281,"navigation":4282,"path":4283,"redirectFrom":4284,"related":4285,"seo":4289,"stem":4290,"subject":583,"summary":4291,"tags":4292,"variables":4298,"__hash__":4316},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz.md","Empirische Varianz",[550,551,552,553,554,555],"Varianz berechnen","Varianz Formel","Stichprobenvarianz","mittlere quadratische Abweichung","s²","n oder n-1 Varianz",{"type":557,"value":558,"toc":4248},"minimark",[559,564,809,991,996,1739,1980,2131,2138,2535,2539,2689,2929,3145,3374,3659,3991,3995],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572,573,664,665,808],"p",{},"Die ",[569,570,571],"strong",{},"Varianz"," misst, wie stark Daten um ihren Mittelwert ",[574,575,578,609],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,604],"semantics",{},[590,591,592],"mrow",{},[593,594,596,600],"mover",{"accent":595},"true",[597,598,599],"mi",{},"x",[601,602,603],"mo",{},"ˉ",[605,606,608],"annotation",{"encoding":607},"application\u002Fx-tex","\\bar{x}",[574,610,613],{"className":611,"ariaHidden":595},[612],"katex-html",[574,614,617,622],{"className":615},[616],"base",[574,618],{"className":619,"style":621},[620],"strut","height:0.5678em;",[574,623,627],{"className":624},[625,626],"mord","accent",[574,628,631],{"className":629},[630],"vlist-t",[574,632,635],{"className":633},[634],"vlist-r",[574,636,639,651],{"className":637,"style":621},[638],"vlist",[574,640,642,647],{"style":641},"top:-3em;",[574,643],{"className":644,"style":646},[645],"pstrut","height:3em;",[574,648,599],{"className":649},[625,650],"mathnormal",[574,652,653,656],{"style":641},[574,654],{"className":655,"style":646},[645],[574,657,661],{"className":658,"style":660},[659],"accent-body","left:-0.2222em;",[574,662,603],{"className":663},[625]," streuen. Man berechnet für jeden Wert die Abweichung ",[574,666,668,697],{"className":667},[577],[574,669,671],{"className":670},[581],[583,672,673],{"xmlns":585},[587,674,675,694],{},[590,676,677,685,688],{},[678,679,680,682],"msub",{},[597,681,599],{},[597,683,684],{},"i",[601,686,687],{},"−",[593,689,690,692],{"accent":595},[597,691,599],{},[601,693,603],{},[605,695,696],{"encoding":607},"x_i - \\bar{x}",[574,698,700,771],{"className":699,"ariaHidden":595},[612],[574,701,703,707,759,764,768],{"className":702},[616],[574,704],{"className":705,"style":706},[620],"height:0.7333em;vertical-align:-0.15em;",[574,708,710,713],{"className":709},[625],[574,711,599],{"className":712},[625,650],[574,714,717],{"className":715},[716],"msupsub",[574,718,721,750],{"className":719},[630,720],"vlist-t2",[574,722,724,745],{"className":723},[634],[574,725,728],{"className":726,"style":727},[638],"height:0.3117em;",[574,729,731,735],{"style":730},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[574,732],{"className":733,"style":734},[645],"height:2.7em;",[574,736,742],{"className":737},[738,739,740,741],"sizing","reset-size6","size3","mtight",[574,743,684],{"className":744},[625,650,741],[574,746,749],{"className":747},[748],"vlist-s","​",[574,751,753],{"className":752},[634],[574,754,757],{"className":755,"style":756},[638],"height:0.15em;",[574,758],{},[574,760],{"className":761,"style":763},[762],"mspace","margin-right:0.2222em;",[574,765,687],{"className":766},[767],"mbin",[574,769],{"className":770,"style":763},[762],[574,772,774,777],{"className":773},[616],[574,775],{"className":776,"style":621},[620],[574,778,780],{"className":779},[625,626],[574,781,783],{"className":782},[630],[574,784,786],{"className":785},[634],[574,787,789,797],{"className":788,"style":621},[638],[574,790,791,794],{"style":641},[574,792],{"className":793,"style":646},[645],[574,795,599],{"className":796},[625,650],[574,798,799,802],{"style":641},[574,800],{"className":801,"style":646},[645],[574,803,805],{"className":804,"style":660},[659],[574,806,603],{"className":807},[625],", quadriert sie und bildet davon den Mittelwert.",[565,810,811,812,990],{},"Das Quadrieren ist nötig, weil sich positive und negative Abweichungen sonst genau aufheben: ",[574,813,815,858],{"className":814},[577],[574,816,818],{"className":817},[581],[583,819,820],{"xmlns":585},[587,821,822,855],{},[590,823,824,827,831,837,839,845,848,851],{},[601,825,826],{},"∑",[601,828,830],{"stretchy":829},"false","(",[678,832,833,835],{},[597,834,599],{},[597,836,684],{},[601,838,687],{},[593,840,841,843],{"accent":595},[597,842,599],{},[601,844,603],{},[601,846,847],{"stretchy":829},")",[601,849,850],{},"=",[852,853,854],"mn",{},"0",[605,856,857],{"encoding":607},"\\sum (x_i - \\bar{x}) = 0",[574,859,861,928,980],{"className":860,"ariaHidden":595},[612],[574,862,864,868,875,879,919,922,925],{"className":863},[616],[574,865],{"className":866,"style":867},[620],"height:1em;vertical-align:-0.25em;",[574,869,826],{"className":870,"style":874},[871,872,873],"mop","op-symbol","small-op","position:relative;top:0em;",[574,876,830],{"className":877},[878],"mopen",[574,880,882,885],{"className":881},[625],[574,883,599],{"className":884},[625,650],[574,886,888],{"className":887},[716],[574,889,891,911],{"className":890},[630,720],[574,892,894,908],{"className":893},[634],[574,895,897],{"className":896,"style":727},[638],[574,898,899,902],{"style":730},[574,900],{"className":901,"style":734},[645],[574,903,905],{"className":904},[738,739,740,741],[574,906,684],{"className":907},[625,650,741],[574,909,749],{"className":910},[748],[574,912,914],{"className":913},[634],[574,915,917],{"className":916,"style":756},[638],[574,918],{},[574,920],{"className":921,"style":763},[762],[574,923,687],{"className":924},[767],[574,926],{"className":927,"style":763},[762],[574,929,931,934,965,969,973,977],{"className":930},[616],[574,932],{"className":933,"style":867},[620],[574,935,937],{"className":936},[625,626],[574,938,940],{"className":939},[630],[574,941,943],{"className":942},[634],[574,944,946,954],{"className":945,"style":621},[638],[574,947,948,951],{"style":641},[574,949],{"className":950,"style":646},[645],[574,952,599],{"className":953},[625,650],[574,955,956,959],{"style":641},[574,957],{"className":958,"style":646},[645],[574,960,962],{"className":961,"style":660},[659],[574,963,603],{"className":964},[625],[574,966,847],{"className":967},[968],"mclose",[574,970],{"className":971,"style":972},[762],"margin-right:0.2778em;",[574,974,850],{"className":975},[976],"mrel",[574,978],{"className":979,"style":972},[762],[574,981,983,987],{"className":982},[616],[574,984],{"className":985,"style":986},[620],"height:0.6444em;",[574,988,854],{"className":989},[625]," gilt immer. Außerdem fallen große Abweichungen dadurch stärker ins Gewicht.",[565,992,993],{},[569,994,995],{},"Achtung, zwei Varianten:",[997,998,999,1324],"ul",{},[1000,1001,1002,1319,1320,1323],"li",{},[574,1003,1005,1061],{"className":1004},[577],[574,1006,1008],{"className":1007},[581],[583,1009,1010],{"xmlns":585},[587,1011,1012,1058],{},[590,1013,1014,1023,1025,1034,1036,1038,1044,1046,1052],{},[1015,1016,1017,1020],"msup",{},[597,1018,1019],{},"s",[852,1021,1022],{},"2",[601,1024,850],{},[1026,1027,1028,1031],"mfrac",{},[852,1029,1030],{},"1",[597,1032,1033],{},"n",[601,1035,826],{},[601,1037,830],{"stretchy":829},[678,1039,1040,1042],{},[597,1041,599],{},[597,1043,684],{},[601,1045,687],{},[593,1047,1048,1050],{"accent":595},[597,1049,599],{},[601,1051,603],{},[1015,1053,1054,1056],{},[601,1055,847],{"stretchy":829},[852,1057,1022],{},[605,1059,1060],{"encoding":607},"s^2 = \\frac{1}{n} \\sum (x_i - \\bar{x})^2",[574,1062,1064,1110,1252],{"className":1063,"ariaHidden":595},[612],[574,1065,1067,1071,1101,1104,1107],{"className":1066},[616],[574,1068],{"className":1069,"style":1070},[620],"height:0.8141em;",[574,1072,1074,1077],{"className":1073},[625],[574,1075,1019],{"className":1076},[625,650],[574,1078,1080],{"className":1079},[716],[574,1081,1083],{"className":1082},[630],[574,1084,1086],{"className":1085},[634],[574,1087,1089],{"className":1088,"style":1070},[638],[574,1090,1092,1095],{"style":1091},"top:-3.063em;margin-right:0.05em;",[574,1093],{"className":1094,"style":734},[645],[574,1096,1098],{"className":1097},[738,739,740,741],[574,1099,1022],{"className":1100},[625,741],[574,1102],{"className":1103,"style":972},[762],[574,1105,850],{"className":1106},[976],[574,1108],{"className":1109,"style":972},[762],[574,1111,1113,1117,1193,1197,1200,1203,1243,1246,1249],{"className":1112},[616],[574,1114],{"className":1115,"style":1116},[620],"height:1.1901em;vertical-align:-0.345em;",[574,1118,1120,1124,1190],{"className":1119},[625],[574,1121],{"className":1122},[878,1123],"nulldelimiter",[574,1125,1127],{"className":1126},[1026],[574,1128,1130,1181],{"className":1129},[630,720],[574,1131,1133,1178],{"className":1132},[634],[574,1134,1137,1152,1163],{"className":1135,"style":1136},[638],"height:0.8451em;",[574,1138,1140,1143],{"style":1139},"top:-2.655em;",[574,1141],{"className":1142,"style":646},[645],[574,1144,1146],{"className":1145},[738,739,740,741],[574,1147,1149],{"className":1148},[625,741],[574,1150,1033],{"className":1151},[625,650,741],[574,1153,1155,1158],{"style":1154},"top:-3.23em;",[574,1156],{"className":1157,"style":646},[645],[574,1159],{"className":1160,"style":1162},[1161],"frac-line","border-bottom-width:0.04em;",[574,1164,1166,1169],{"style":1165},"top:-3.394em;",[574,1167],{"className":1168,"style":646},[645],[574,1170,1172],{"className":1171},[738,739,740,741],[574,1173,1175],{"className":1174},[625,741],[574,1176,1030],{"className":1177},[625,741],[574,1179,749],{"className":1180},[748],[574,1182,1184],{"className":1183},[634],[574,1185,1188],{"className":1186,"style":1187},[638],"height:0.345em;",[574,1189],{},[574,1191],{"className":1192},[968,1123],[574,1194],{"className":1195,"style":1196},[762],"margin-right:0.1667em;",[574,1198,826],{"className":1199,"style":874},[871,872,873],[574,1201,830],{"className":1202},[878],[574,1204,1206,1209],{"className":1205},[625],[574,1207,599],{"className":1208},[625,650],[574,1210,1212],{"className":1211},[716],[574,1213,1215,1235],{"className":1214},[630,720],[574,1216,1218,1232],{"className":1217},[634],[574,1219,1221],{"className":1220,"style":727},[638],[574,1222,1223,1226],{"style":730},[574,1224],{"className":1225,"style":734},[645],[574,1227,1229],{"className":1228},[738,739,740,741],[574,1230,684],{"className":1231},[625,650,741],[574,1233,749],{"className":1234},[748],[574,1236,1238],{"className":1237},[634],[574,1239,1241],{"className":1240,"style":756},[638],[574,1242],{},[574,1244],{"className":1245,"style":763},[762],[574,1247,687],{"className":1248},[767],[574,1250],{"className":1251,"style":763},[762],[574,1253,1255,1259,1290],{"className":1254},[616],[574,1256],{"className":1257,"style":1258},[620],"height:1.0641em;vertical-align:-0.25em;",[574,1260,1262],{"className":1261},[625,626],[574,1263,1265],{"className":1264},[630],[574,1266,1268],{"className":1267},[634],[574,1269,1271,1279],{"className":1270,"style":621},[638],[574,1272,1273,1276],{"style":641},[574,1274],{"className":1275,"style":646},[645],[574,1277,599],{"className":1278},[625,650],[574,1280,1281,1284],{"style":641},[574,1282],{"className":1283,"style":646},[645],[574,1285,1287],{"className":1286,"style":660},[659],[574,1288,603],{"className":1289},[625],[574,1291,1293,1296],{"className":1292},[968],[574,1294,847],{"className":1295},[968],[574,1297,1299],{"className":1298},[716],[574,1300,1302],{"className":1301},[630],[574,1303,1305],{"className":1304},[634],[574,1306,1308],{"className":1307,"style":1070},[638],[574,1309,1310,1313],{"style":1091},[574,1311],{"className":1312,"style":734},[645],[574,1314,1316],{"className":1315},[738,739,740,741],[574,1317,1022],{"className":1318},[625,741]," beschreibt die Streuung der vorliegenden Daten selbst. Diese Form steht hier und wird in der Schule meist ",[569,1321,1322],{},"empirische Varianz"," genannt.",[1000,1325,1326,1681,1682,1735,1736,1738],{},[574,1327,1329,1394],{"className":1328},[577],[574,1330,1332],{"className":1331},[581],[583,1333,1334],{"xmlns":585},[587,1335,1336,1391],{},[590,1337,1338,1353,1355,1367,1369,1371,1377,1379,1385],{},[1339,1340,1341,1343,1351],"msubsup",{},[597,1342,1019],{},[590,1344,1345,1347,1349],{},[597,1346,1033],{},[601,1348,687],{},[852,1350,1030],{},[852,1352,1022],{},[601,1354,850],{},[1026,1356,1357,1359],{},[852,1358,1030],{},[590,1360,1361,1363,1365],{},[597,1362,1033],{},[601,1364,687],{},[852,1366,1030],{},[601,1368,826],{},[601,1370,830],{"stretchy":829},[678,1372,1373,1375],{},[597,1374,599],{},[597,1376,684],{},[601,1378,687],{},[593,1380,1381,1383],{"accent":595},[597,1382,599],{},[601,1384,603],{},[1015,1386,1387,1389],{},[601,1388,847],{"stretchy":829},[852,1390,1022],{},[605,1392,1393],{"encoding":607},"s_{n-1}^2 = \\frac{1}{n-1} \\sum (x_i - \\bar{x})^2",[574,1395,1397,1475,1615],{"className":1396,"ariaHidden":595},[612],[574,1398,1400,1404,1466,1469,1472],{"className":1399},[616],[574,1401],{"className":1402,"style":1403},[620],"height:1.1205em;vertical-align:-0.3064em;",[574,1405,1407,1410],{"className":1406},[625],[574,1408,1019],{"className":1409},[625,650],[574,1411,1413],{"className":1412},[716],[574,1414,1416,1457],{"className":1415},[630,720],[574,1417,1419,1454],{"className":1418},[634],[574,1420,1422,1443],{"className":1421,"style":1070},[638],[574,1423,1425,1428],{"style":1424},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[574,1426],{"className":1427,"style":734},[645],[574,1429,1431],{"className":1430},[738,739,740,741],[574,1432,1434,1437,1440],{"className":1433},[625,741],[574,1435,1033],{"className":1436},[625,650,741],[574,1438,687],{"className":1439},[767,741],[574,1441,1030],{"className":1442},[625,741],[574,1444,1445,1448],{"style":1091},[574,1446],{"className":1447,"style":734},[645],[574,1449,1451],{"className":1450},[738,739,740,741],[574,1452,1022],{"className":1453},[625,741],[574,1455,749],{"className":1456},[748],[574,1458,1460],{"className":1459},[634],[574,1461,1464],{"className":1462,"style":1463},[638],"height:0.3064em;",[574,1465],{},[574,1467],{"className":1468,"style":972},[762],[574,1470,850],{"className":1471},[976],[574,1473],{"className":1474,"style":972},[762],[574,1476,1478,1482,1557,1560,1563,1566,1606,1609,1612],{"className":1477},[616],[574,1479],{"className":1480,"style":1481},[620],"height:1.2484em;vertical-align:-0.4033em;",[574,1483,1485,1488,1554],{"className":1484},[625],[574,1486],{"className":1487},[878,1123],[574,1489,1491],{"className":1490},[1026],[574,1492,1494,1545],{"className":1493},[630,720],[574,1495,1497,1542],{"className":1496},[634],[574,1498,1500,1520,1528],{"className":1499,"style":1136},[638],[574,1501,1502,1505],{"style":1139},[574,1503],{"className":1504,"style":646},[645],[574,1506,1508],{"className":1507},[738,739,740,741],[574,1509,1511,1514,1517],{"className":1510},[625,741],[574,1512,1033],{"className":1513},[625,650,741],[574,1515,687],{"className":1516},[767,741],[574,1518,1030],{"className":1519},[625,741],[574,1521,1522,1525],{"style":1154},[574,1523],{"className":1524,"style":646},[645],[574,1526],{"className":1527,"style":1162},[1161],[574,1529,1530,1533],{"style":1165},[574,1531],{"className":1532,"style":646},[645],[574,1534,1536],{"className":1535},[738,739,740,741],[574,1537,1539],{"className":1538},[625,741],[574,1540,1030],{"className":1541},[625,741],[574,1543,749],{"className":1544},[748],[574,1546,1548],{"className":1547},[634],[574,1549,1552],{"className":1550,"style":1551},[638],"height:0.4033em;",[574,1553],{},[574,1555],{"className":1556},[968,1123],[574,1558],{"className":1559,"style":1196},[762],[574,1561,826],{"className":1562,"style":874},[871,872,873],[574,1564,830],{"className":1565},[878],[574,1567,1569,1572],{"className":1568},[625],[574,1570,599],{"className":1571},[625,650],[574,1573,1575],{"className":1574},[716],[574,1576,1578,1598],{"className":1577},[630,720],[574,1579,1581,1595],{"className":1580},[634],[574,1582,1584],{"className":1583,"style":727},[638],[574,1585,1586,1589],{"style":730},[574,1587],{"className":1588,"style":734},[645],[574,1590,1592],{"className":1591},[738,739,740,741],[574,1593,684],{"className":1594},[625,650,741],[574,1596,749],{"className":1597},[748],[574,1599,1601],{"className":1600},[634],[574,1602,1604],{"className":1603,"style":756},[638],[574,1605],{},[574,1607],{"className":1608,"style":763},[762],[574,1610,687],{"className":1611},[767],[574,1613],{"className":1614,"style":763},[762],[574,1616,1618,1621,1652],{"className":1617},[616],[574,1619],{"className":1620,"style":1258},[620],[574,1622,1624],{"className":1623},[625,626],[574,1625,1627],{"className":1626},[630],[574,1628,1630],{"className":1629},[634],[574,1631,1633,1641],{"className":1632,"style":621},[638],[574,1634,1635,1638],{"style":641},[574,1636],{"className":1637,"style":646},[645],[574,1639,599],{"className":1640},[625,650],[574,1642,1643,1646],{"style":641},[574,1644],{"className":1645,"style":646},[645],[574,1647,1649],{"className":1648,"style":660},[659],[574,1650,603],{"className":1651},[625],[574,1653,1655,1658],{"className":1654},[968],[574,1656,847],{"className":1657},[968],[574,1659,1661],{"className":1660},[716],[574,1662,1664],{"className":1663},[630],[574,1665,1667],{"className":1666},[634],[574,1668,1670],{"className":1669,"style":1070},[638],[574,1671,1672,1675],{"style":1091},[574,1673],{"className":1674,"style":734},[645],[574,1676,1678],{"className":1677},[738,739,740,741],[574,1679,1022],{"className":1680},[625,741]," (für ",[574,1683,1685,1704],{"className":1684},[577],[574,1686,1688],{"className":1687},[581],[583,1689,1690],{"xmlns":585},[587,1691,1692,1701],{},[590,1693,1694,1696,1699],{},[597,1695,1033],{},[601,1697,1698],{},"≥",[852,1700,1022],{},[605,1702,1703],{"encoding":607},"n \\geq 2",[574,1705,1707,1726],{"className":1706,"ariaHidden":595},[612],[574,1708,1710,1714,1717,1720,1723],{"className":1709},[616],[574,1711],{"className":1712,"style":1713},[620],"height:0.7719em;vertical-align:-0.136em;",[574,1715,1033],{"className":1716},[625,650],[574,1718],{"className":1719,"style":972},[762],[574,1721,1698],{"className":1722},[976],[574,1724],{"className":1725,"style":972},[762],[574,1727,1729,1732],{"className":1728},[616],[574,1730],{"className":1731,"style":986},[620],[574,1733,1022],{"className":1734},[625],") heißt ",[569,1737,552],{}," oder korrigierte Varianz. Man nimmt sie, wenn die Daten eine Stichprobe sind und man damit die Varianz der ganzen Grundgesamtheit schätzen will.",[565,1740,1741,1742,1817,1818,1847,1848,1817,1918,1979],{},"Die Bezeichnungen sind in Büchern und auf Taschenrechnern nicht einheitlich (oft ",[574,1743,1745,1764],{"className":1744},[577],[574,1746,1748],{"className":1747},[581],[583,1749,1750],{"xmlns":585},[587,1751,1752,1761],{},[590,1753,1754],{},[678,1755,1756,1759],{},[597,1757,1758],{},"σ",[597,1760,599],{},[605,1762,1763],{"encoding":607},"\\sigma_x",[574,1765,1767],{"className":1766,"ariaHidden":595},[612],[574,1768,1770,1774],{"className":1769},[616],[574,1771],{"className":1772,"style":1773},[620],"height:0.5806em;vertical-align:-0.15em;",[574,1775,1777,1781],{"className":1776},[625],[574,1778,1758],{"className":1779,"style":1780},[625,650],"margin-right:0.0359em;",[574,1782,1784],{"className":1783},[716],[574,1785,1787,1809],{"className":1786},[630,720],[574,1788,1790,1806],{"className":1789},[634],[574,1791,1794],{"className":1792,"style":1793},[638],"height:0.1514em;",[574,1795,1797,1800],{"style":1796},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[574,1798],{"className":1799,"style":734},[645],[574,1801,1803],{"className":1802},[738,739,740,741],[574,1804,599],{"className":1805},[625,650,741],[574,1807,749],{"className":1808},[748],[574,1810,1812],{"className":1811},[634],[574,1813,1815],{"className":1814,"style":756},[638],[574,1816],{}," für die ",[574,1819,1821,1834],{"className":1820},[577],[574,1822,1824],{"className":1823},[581],[583,1825,1826],{"xmlns":585},[587,1827,1828,1832],{},[590,1829,1830],{},[597,1831,1033],{},[605,1833,1033],{"encoding":607},[574,1835,1837],{"className":1836,"ariaHidden":595},[612],[574,1838,1840,1844],{"className":1839},[616],[574,1841],{"className":1842,"style":1843},[620],"height:0.4306em;",[574,1845,1033],{"className":1846},[625,650],"-Variante und ",[574,1849,1851,1869],{"className":1850},[577],[574,1852,1854],{"className":1853},[581],[583,1855,1856],{"xmlns":585},[587,1857,1858,1866],{},[590,1859,1860],{},[678,1861,1862,1864],{},[597,1863,1019],{},[597,1865,599],{},[605,1867,1868],{"encoding":607},"s_x",[574,1870,1872],{"className":1871,"ariaHidden":595},[612],[574,1873,1875,1878],{"className":1874},[616],[574,1876],{"className":1877,"style":1773},[620],[574,1879,1881,1884],{"className":1880},[625],[574,1882,1019],{"className":1883},[625,650],[574,1885,1887],{"className":1886},[716],[574,1888,1890,1910],{"className":1889},[630,720],[574,1891,1893,1907],{"className":1892},[634],[574,1894,1896],{"className":1895,"style":1793},[638],[574,1897,1898,1901],{"style":730},[574,1899],{"className":1900,"style":734},[645],[574,1902,1904],{"className":1903},[738,739,740,741],[574,1905,599],{"className":1906},[625,650,741],[574,1908,749],{"className":1909},[748],[574,1911,1913],{"className":1912},[634],[574,1914,1916],{"className":1915,"style":756},[638],[574,1917],{},[574,1919,1921,1943],{"className":1920},[577],[574,1922,1924],{"className":1923},[581],[583,1925,1926],{"xmlns":585},[587,1927,1928,1940],{},[590,1929,1930,1932,1934,1936,1938],{},[601,1931,830],{"stretchy":829},[597,1933,1033],{},[601,1935,687],{},[852,1937,1030],{},[601,1939,847],{"stretchy":829},[605,1941,1942],{"encoding":607},"(n-1)",[574,1944,1946,1967],{"className":1945,"ariaHidden":595},[612],[574,1947,1949,1952,1955,1958,1961,1964],{"className":1948},[616],[574,1950],{"className":1951,"style":867},[620],[574,1953,830],{"className":1954},[878],[574,1956,1033],{"className":1957},[625,650],[574,1959],{"className":1960,"style":763},[762],[574,1962,687],{"className":1963},[767],[574,1965],{"className":1966,"style":763},[762],[574,1968,1970,1973,1976],{"className":1969},[616],[574,1971],{"className":1972,"style":867},[620],[574,1974,1030],{"className":1975},[625],[574,1977,847],{"className":1978},[968],"-Variante). Deshalb immer angeben, durch was geteilt wird.",[565,1981,1982,1983,2130],{},"Die Einheit der Varianz ist das Quadrat der Dateneinheit. Eine anschaulichere Größe ist die Standardabweichung ",[574,1984,1986,2011],{"className":1985},[577],[574,1987,1989],{"className":1988},[581],[583,1990,1991],{"xmlns":585},[587,1992,1993,2008],{},[590,1994,1995,1997,1999],{},[597,1996,1019],{},[601,1998,850],{},[2000,2001,2002],"msqrt",{},[1015,2003,2004,2006],{},[597,2005,1019],{},[852,2007,1022],{},[605,2009,2010],{"encoding":607},"s = \\sqrt{s^2}",[574,2012,2014,2032],{"className":2013,"ariaHidden":595},[612],[574,2015,2017,2020,2023,2026,2029],{"className":2016},[616],[574,2018],{"className":2019,"style":1843},[620],[574,2021,1019],{"className":2022},[625,650],[574,2024],{"className":2025,"style":972},[762],[574,2027,850],{"className":2028},[976],[574,2030],{"className":2031,"style":972},[762],[574,2033,2035,2039],{"className":2034},[616],[574,2036],{"className":2037,"style":2038},[620],"height:1.04em;vertical-align:-0.0849em;",[574,2040,2043],{"className":2041},[625,2042],"sqrt",[574,2044,2046,2121],{"className":2045},[630,720],[574,2047,2049,2118],{"className":2048},[634],[574,2050,2053,2095],{"className":2051,"style":2052},[638],"height:0.9551em;",[574,2054,2057,2060],{"className":2055,"style":641},[2056],"svg-align",[574,2058],{"className":2059,"style":646},[645],[574,2061,2064],{"className":2062,"style":2063},[625],"padding-left:0.833em;",[574,2065,2067,2070],{"className":2066},[625],[574,2068,1019],{"className":2069},[625,650],[574,2071,2073],{"className":2072},[716],[574,2074,2076],{"className":2075},[630],[574,2077,2079],{"className":2078},[634],[574,2080,2083],{"className":2081,"style":2082},[638],"height:0.7401em;",[574,2084,2086,2089],{"style":2085},"top:-2.989em;margin-right:0.05em;",[574,2087],{"className":2088,"style":734},[645],[574,2090,2092],{"className":2091},[738,739,740,741],[574,2093,1022],{"className":2094},[625,741],[574,2096,2098,2101],{"style":2097},"top:-2.9151em;",[574,2099],{"className":2100,"style":646},[645],[574,2102,2106],{"className":2103,"style":2105},[2104],"hide-tail","min-width:0.853em;height:1.08em;",[2107,2108,2114],"svg",{"xmlns":2109,"width":2110,"height":2111,"viewBox":2112,"preserveAspectRatio":2113},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[2115,2116],"path",{"d":2117},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[574,2119,749],{"className":2120},[748],[574,2122,2124],{"className":2123},[634],[574,2125,2128],{"className":2126,"style":2127},[638],"height:0.0849em;",[574,2129],{},".",[565,2132,2133,2134,2137],{},"Oft schneller ist der ",[569,2135,2136],{},"Verschiebungssatz",": Mittelwert der Quadrate minus Quadrat des Mittelwerts,",[574,2139,2142],{"className":2140},[2141],"katex-display",[574,2143,2145,2207],{"className":2144},[577],[574,2146,2148],{"className":2147},[581],[583,2149,2151],{"xmlns":585,"display":2150},"block",[587,2152,2153,2204],{},[590,2154,2155,2161,2163,2169,2184,2192,2194],{},[1015,2156,2157,2159],{},[597,2158,1019],{},[852,2160,1022],{},[601,2162,850],{},[1026,2164,2165,2167],{},[852,2166,1030],{},[597,2168,1033],{},[2170,2171,2172,2174,2182],"munderover",{},[601,2173,826],{},[590,2175,2176,2178,2180],{},[597,2177,684],{},[601,2179,850],{},[852,2181,1030],{},[597,2183,1033],{},[1339,2185,2186,2188,2190],{},[597,2187,599],{},[597,2189,684],{},[852,2191,1022],{},[601,2193,687],{},[1015,2195,2196,2202],{},[593,2197,2198,2200],{"accent":595},[597,2199,599],{},[601,2201,603],{},[852,2203,1022],{},[605,2205,2206],{"encoding":607},"s^2 = \\frac{1}{n} \\sum_{i=1}^{n} x_i^2 - \\bar{x}^2",[574,2208,2210,2256,2472],{"className":2209,"ariaHidden":595},[612],[574,2211,2213,2217,2247,2250,2253],{"className":2212},[616],[574,2214],{"className":2215,"style":2216},[620],"height:0.8641em;",[574,2218,2220,2223],{"className":2219},[625],[574,2221,1019],{"className":2222},[625,650],[574,2224,2226],{"className":2225},[716],[574,2227,2229],{"className":2228},[630],[574,2230,2232],{"className":2231},[634],[574,2233,2235],{"className":2234,"style":2216},[638],[574,2236,2238,2241],{"style":2237},"top:-3.113em;margin-right:0.05em;",[574,2239],{"className":2240,"style":734},[645],[574,2242,2244],{"className":2243},[738,739,740,741],[574,2245,1022],{"className":2246},[625,741],[574,2248],{"className":2249,"style":972},[762],[574,2251,850],{"className":2252},[976],[574,2254],{"className":2255,"style":972},[762],[574,2257,2259,2263,2329,2332,2407,2410,2463,2466,2469],{"className":2258},[616],[574,2260],{"className":2261,"style":2262},[620],"height:2.9291em;vertical-align:-1.2777em;",[574,2264,2266,2269,2326],{"className":2265},[625],[574,2267],{"className":2268},[878,1123],[574,2270,2272],{"className":2271},[1026],[574,2273,2275,2317],{"className":2274},[630,720],[574,2276,2278,2314],{"className":2277},[634],[574,2279,2282,2294,2302],{"className":2280,"style":2281},[638],"height:1.3214em;",[574,2283,2285,2288],{"style":2284},"top:-2.314em;",[574,2286],{"className":2287,"style":646},[645],[574,2289,2291],{"className":2290},[625],[574,2292,1033],{"className":2293},[625,650],[574,2295,2296,2299],{"style":1154},[574,2297],{"className":2298,"style":646},[645],[574,2300],{"className":2301,"style":1162},[1161],[574,2303,2305,2308],{"style":2304},"top:-3.677em;",[574,2306],{"className":2307,"style":646},[645],[574,2309,2311],{"className":2310},[625],[574,2312,1030],{"className":2313},[625],[574,2315,749],{"className":2316},[748],[574,2318,2320],{"className":2319},[634],[574,2321,2324],{"className":2322,"style":2323},[638],"height:0.686em;",[574,2325],{},[574,2327],{"className":2328},[968,1123],[574,2330],{"className":2331,"style":1196},[762],[574,2333,2336],{"className":2334},[871,2335],"op-limits",[574,2337,2339,2398],{"className":2338},[630,720],[574,2340,2342,2395],{"className":2341},[634],[574,2343,2346,2368,2380],{"className":2344,"style":2345},[638],"height:1.6514em;",[574,2347,2349,2353],{"style":2348},"top:-1.8723em;margin-left:0em;",[574,2350],{"className":2351,"style":2352},[645],"height:3.05em;",[574,2354,2356],{"className":2355},[738,739,740,741],[574,2357,2359,2362,2365],{"className":2358},[625,741],[574,2360,684],{"className":2361},[625,650,741],[574,2363,850],{"className":2364},[976,741],[574,2366,1030],{"className":2367},[625,741],[574,2369,2371,2374],{"style":2370},"top:-3.05em;",[574,2372],{"className":2373,"style":2352},[645],[574,2375,2376],{},[574,2377,826],{"className":2378},[871,872,2379],"large-op",[574,2381,2383,2386],{"style":2382},"top:-4.3em;margin-left:0em;",[574,2384],{"className":2385,"style":2352},[645],[574,2387,2389],{"className":2388},[738,739,740,741],[574,2390,2392],{"className":2391},[625,741],[574,2393,1033],{"className":2394},[625,650,741],[574,2396,749],{"className":2397},[748],[574,2399,2401],{"className":2400},[634],[574,2402,2405],{"className":2403,"style":2404},[638],"height:1.2777em;",[574,2406],{},[574,2408],{"className":2409,"style":1196},[762],[574,2411,2413,2416],{"className":2412},[625],[574,2414,599],{"className":2415},[625,650],[574,2417,2419],{"className":2418},[716],[574,2420,2422,2454],{"className":2421},[630,720],[574,2423,2425,2451],{"className":2424},[634],[574,2426,2428,2440],{"className":2427,"style":2216},[638],[574,2429,2431,2434],{"style":2430},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[574,2432],{"className":2433,"style":734},[645],[574,2435,2437],{"className":2436},[738,739,740,741],[574,2438,684],{"className":2439},[625,650,741],[574,2441,2442,2445],{"style":2237},[574,2443],{"className":2444,"style":734},[645],[574,2446,2448],{"className":2447},[738,739,740,741],[574,2449,1022],{"className":2450},[625,741],[574,2452,749],{"className":2453},[748],[574,2455,2457],{"className":2456},[634],[574,2458,2461],{"className":2459,"style":2460},[638],"height:0.247em;",[574,2462],{},[574,2464],{"className":2465,"style":763},[762],[574,2467,687],{"className":2468},[767],[574,2470],{"className":2471,"style":763},[762],[574,2473,2475,2478],{"className":2474},[616],[574,2476],{"className":2477,"style":2216},[620],[574,2479,2481,2512],{"className":2480},[625],[574,2482,2484],{"className":2483},[625,626],[574,2485,2487],{"className":2486},[630],[574,2488,2490],{"className":2489},[634],[574,2491,2493,2501],{"className":2492,"style":621},[638],[574,2494,2495,2498],{"style":641},[574,2496],{"className":2497,"style":646},[645],[574,2499,599],{"className":2500},[625,650],[574,2502,2503,2506],{"style":641},[574,2504],{"className":2505,"style":646},[645],[574,2507,2509],{"className":2508,"style":660},[659],[574,2510,603],{"className":2511},[625],[574,2513,2515],{"className":2514},[716],[574,2516,2518],{"className":2517},[630],[574,2519,2521],{"className":2520},[634],[574,2522,2524],{"className":2523,"style":2216},[638],[574,2525,2526,2529],{"style":2237},[574,2527],{"className":2528,"style":734},[645],[574,2530,2532],{"className":2531},[738,739,740,741],[574,2533,1022],{"className":2534},[625,741],[560,2536,2538],{"id":2537},"beispiele","Beispiele",[565,2540,2541,2542,2571,2572,2571,2601,2571,2630,2659,2660,2688],{},"An fünf Tagen wartet Ben an der Haltestelle ",[574,2543,2545,2559],{"className":2544},[577],[574,2546,2548],{"className":2547},[581],[583,2549,2550],{"xmlns":585},[587,2551,2552,2557],{},[590,2553,2554],{},[852,2555,2556],{},"4",[605,2558,2556],{"encoding":607},[574,2560,2562],{"className":2561,"ariaHidden":595},[612],[574,2563,2565,2568],{"className":2564},[616],[574,2566],{"className":2567,"style":986},[620],[574,2569,2556],{"className":2570},[625],", ",[574,2573,2575,2589],{"className":2574},[577],[574,2576,2578],{"className":2577},[581],[583,2579,2580],{"xmlns":585},[587,2581,2582,2587],{},[590,2583,2584],{},[852,2585,2586],{},"7",[605,2588,2586],{"encoding":607},[574,2590,2592],{"className":2591,"ariaHidden":595},[612],[574,2593,2595,2598],{"className":2594},[616],[574,2596],{"className":2597,"style":986},[620],[574,2599,2586],{"className":2600},[625],[574,2602,2604,2618],{"className":2603},[577],[574,2605,2607],{"className":2606},[581],[583,2608,2609],{"xmlns":585},[587,2610,2611,2616],{},[590,2612,2613],{},[852,2614,2615],{},"5",[605,2617,2615],{"encoding":607},[574,2619,2621],{"className":2620,"ariaHidden":595},[612],[574,2622,2624,2627],{"className":2623},[616],[574,2625],{"className":2626,"style":986},[620],[574,2628,2615],{"className":2629},[625],[574,2631,2633,2647],{"className":2632},[577],[574,2634,2636],{"className":2635},[581],[583,2637,2638],{"xmlns":585},[587,2639,2640,2645],{},[590,2641,2642],{},[852,2643,2644],{},"9",[605,2646,2644],{"encoding":607},[574,2648,2650],{"className":2649,"ariaHidden":595},[612],[574,2651,2653,2656],{"className":2652},[616],[574,2654],{"className":2655,"style":986},[620],[574,2657,2644],{"className":2658},[625]," und ",[574,2661,2663,2676],{"className":2662},[577],[574,2664,2666],{"className":2665},[581],[583,2667,2668],{"xmlns":585},[587,2669,2670,2674],{},[590,2671,2672],{},[852,2673,2615],{},[605,2675,2615],{"encoding":607},[574,2677,2679],{"className":2678,"ariaHidden":595},[612],[574,2680,2682,2685],{"className":2681},[616],[574,2683],{"className":2684,"style":986},[620],[574,2686,2615],{"className":2687},[625]," Minuten. Mittelwert:",[574,2690,2692],{"className":2691},[2141],[574,2693,2695,2745],{"className":2694},[577],[574,2696,2698],{"className":2697},[581],[583,2699,2700],{"xmlns":585,"display":2150},[587,2701,2702,2742],{},[590,2703,2704,2710,2712,2737,2739],{},[593,2705,2706,2708],{"accent":595},[597,2707,599],{},[601,2709,603],{},[601,2711,850],{},[1026,2713,2714,2735],{},[590,2715,2716,2718,2721,2723,2725,2727,2729,2731,2733],{},[852,2717,2556],{},[601,2719,2720],{},"+",[852,2722,2586],{},[601,2724,2720],{},[852,2726,2615],{},[601,2728,2720],{},[852,2730,2644],{},[601,2732,2720],{},[852,2734,2615],{},[852,2736,2615],{},[601,2738,850],{},[852,2740,2741],{},"6",[605,2743,2744],{"encoding":607},"\\bar{x} = \\frac{4 + 7 + 5 + 9 + 5}{5} = 6",[574,2746,2748,2794,2920],{"className":2747,"ariaHidden":595},[612],[574,2749,2751,2754,2785,2788,2791],{"className":2750},[616],[574,2752],{"className":2753,"style":621},[620],[574,2755,2757],{"className":2756},[625,626],[574,2758,2760],{"className":2759},[630],[574,2761,2763],{"className":2762},[634],[574,2764,2766,2774],{"className":2765,"style":621},[638],[574,2767,2768,2771],{"style":641},[574,2769],{"className":2770,"style":646},[645],[574,2772,599],{"className":2773},[625,650],[574,2775,2776,2779],{"style":641},[574,2777],{"className":2778,"style":646},[645],[574,2780,2782],{"className":2781,"style":660},[659],[574,2783,603],{"className":2784},[625],[574,2786],{"className":2787,"style":972},[762],[574,2789,850],{"className":2790},[976],[574,2792],{"className":2793,"style":972},[762],[574,2795,2797,2801,2911,2914,2917],{"className":2796},[616],[574,2798],{"className":2799,"style":2800},[620],"height:2.0074em;vertical-align:-0.686em;",[574,2802,2804,2807,2908],{"className":2803},[625],[574,2805],{"className":2806},[878,1123],[574,2808,2810],{"className":2809},[1026],[574,2811,2813,2900],{"className":2812},[630,720],[574,2814,2816,2897],{"className":2815},[634],[574,2817,2819,2830,2838],{"className":2818,"style":2281},[638],[574,2820,2821,2824],{"style":2284},[574,2822],{"className":2823,"style":646},[645],[574,2825,2827],{"className":2826},[625],[574,2828,2615],{"className":2829},[625],[574,2831,2832,2835],{"style":1154},[574,2833],{"className":2834,"style":646},[645],[574,2836],{"className":2837,"style":1162},[1161],[574,2839,2840,2843],{"style":2304},[574,2841],{"className":2842,"style":646},[645],[574,2844,2846,2849,2852,2855,2858,2861,2864,2867,2870,2873,2876,2879,2882,2885,2888,2891,2894],{"className":2845},[625],[574,2847,2556],{"className":2848},[625],[574,2850],{"className":2851,"style":763},[762],[574,2853,2720],{"className":2854},[767],[574,2856],{"className":2857,"style":763},[762],[574,2859,2586],{"className":2860},[625],[574,2862],{"className":2863,"style":763},[762],[574,2865,2720],{"className":2866},[767],[574,2868],{"className":2869,"style":763},[762],[574,2871,2615],{"className":2872},[625],[574,2874],{"className":2875,"style":763},[762],[574,2877,2720],{"className":2878},[767],[574,2880],{"className":2881,"style":763},[762],[574,2883,2644],{"className":2884},[625],[574,2886],{"className":2887,"style":763},[762],[574,2889,2720],{"className":2890},[767],[574,2892],{"className":2893,"style":763},[762],[574,2895,2615],{"className":2896},[625],[574,2898,749],{"className":2899},[748],[574,2901,2903],{"className":2902},[634],[574,2904,2906],{"className":2905,"style":2323},[638],[574,2907],{},[574,2909],{"className":2910},[968,1123],[574,2912],{"className":2913,"style":972},[762],[574,2915,850],{"className":2916},[976],[574,2918],{"className":2919,"style":972},[762],[574,2921,2923,2926],{"className":2922},[616],[574,2924],{"className":2925,"style":986},[620],[574,2927,2741],{"className":2928},[625],[565,2930,2931,2932,3032,3033,3114,3115,3144],{},"Die Abweichungen sind ",[574,2933,2935,2973],{"className":2934},[577],[574,2936,2938],{"className":2937},[581],[583,2939,2940],{"xmlns":585},[587,2941,2942,2970],{},[590,2943,2944,2946,2948,2951,2953,2955,2957,2959,2961,2964,2966,2968],{},[601,2945,687],{},[852,2947,1022],{},[601,2949,2950],{"separator":595},",",[852,2952,1030],{},[601,2954,2950],{"separator":595},[601,2956,687],{},[852,2958,1030],{},[601,2960,2950],{"separator":595},[852,2962,2963],{},"3",[601,2965,2950],{"separator":595},[601,2967,687],{},[852,2969,1030],{},[605,2971,2972],{"encoding":607},"-2, 1, -1, 3, -1",[574,2974,2976],{"className":2975,"ariaHidden":595},[612],[574,2977,2979,2983,2986,2989,2993,2996,2999,3002,3005,3008,3011,3014,3017,3020,3023,3026,3029],{"className":2978},[616],[574,2980],{"className":2981,"style":2982},[620],"height:0.8389em;vertical-align:-0.1944em;",[574,2984,687],{"className":2985},[625],[574,2987,1022],{"className":2988},[625],[574,2990,2950],{"className":2991},[2992],"mpunct",[574,2994],{"className":2995,"style":1196},[762],[574,2997,1030],{"className":2998},[625],[574,3000,2950],{"className":3001},[2992],[574,3003],{"className":3004,"style":1196},[762],[574,3006,687],{"className":3007},[625],[574,3009,1030],{"className":3010},[625],[574,3012,2950],{"className":3013},[2992],[574,3015],{"className":3016,"style":1196},[762],[574,3018,2963],{"className":3019},[625],[574,3021,2950],{"className":3022},[2992],[574,3024],{"className":3025,"style":1196},[762],[574,3027,687],{"className":3028},[625],[574,3030,1030],{"className":3031},[625],", ihre Quadrate ",[574,3034,3036,3066],{"className":3035},[577],[574,3037,3039],{"className":3038},[581],[583,3040,3041],{"xmlns":585},[587,3042,3043,3063],{},[590,3044,3045,3047,3049,3051,3053,3055,3057,3059,3061],{},[852,3046,2556],{},[601,3048,2950],{"separator":595},[852,3050,1030],{},[601,3052,2950],{"separator":595},[852,3054,1030],{},[601,3056,2950],{"separator":595},[852,3058,2644],{},[601,3060,2950],{"separator":595},[852,3062,1030],{},[605,3064,3065],{"encoding":607},"4, 1, 1, 9, 1",[574,3067,3069],{"className":3068,"ariaHidden":595},[612],[574,3070,3072,3075,3078,3081,3084,3087,3090,3093,3096,3099,3102,3105,3108,3111],{"className":3071},[616],[574,3073],{"className":3074,"style":2982},[620],[574,3076,2556],{"className":3077},[625],[574,3079,2950],{"className":3080},[2992],[574,3082],{"className":3083,"style":1196},[762],[574,3085,1030],{"className":3086},[625],[574,3088,2950],{"className":3089},[2992],[574,3091],{"className":3092,"style":1196},[762],[574,3094,1030],{"className":3095},[625],[574,3097,2950],{"className":3098},[2992],[574,3100],{"className":3101,"style":1196},[762],[574,3103,2644],{"className":3104},[625],[574,3106,2950],{"className":3107},[2992],[574,3109],{"className":3110,"style":1196},[762],[574,3112,1030],{"className":3113},[625]," mit Summe ",[574,3116,3118,3132],{"className":3117},[577],[574,3119,3121],{"className":3120},[581],[583,3122,3123],{"xmlns":585},[587,3124,3125,3130],{},[590,3126,3127],{},[852,3128,3129],{},"16",[605,3131,3129],{"encoding":607},[574,3133,3135],{"className":3134,"ariaHidden":595},[612],[574,3136,3138,3141],{"className":3137},[616],[574,3139],{"className":3140,"style":986},[620],[574,3142,3129],{"className":3143},[625],":",[574,3146,3148],{"className":3147},[2141],[574,3149,3151,3193],{"className":3150},[577],[574,3152,3154],{"className":3153},[581],[583,3155,3156],{"xmlns":585,"display":2150},[587,3157,3158,3190],{},[590,3159,3160,3166,3168,3174,3176,3179,3183],{},[1015,3161,3162,3164],{},[597,3163,1019],{},[852,3165,1022],{},[601,3167,850],{},[1026,3169,3170,3172],{},[852,3171,3129],{},[852,3173,2615],{},[601,3175,850],{},[852,3177,3178],{},"3,2",[3180,3181,3182],"mtext",{}," ",[1015,3184,3185,3188],{},[3180,3186,3187],{},"min",[852,3189,1022],{},[605,3191,3192],{"encoding":607},"s^2 = \\frac{16}{5} = 3{,}2\\,\\text{min}^2",[574,3194,3196,3240,3317],{"className":3195,"ariaHidden":595},[612],[574,3197,3199,3202,3231,3234,3237],{"className":3198},[616],[574,3200],{"className":3201,"style":2216},[620],[574,3203,3205,3208],{"className":3204},[625],[574,3206,1019],{"className":3207},[625,650],[574,3209,3211],{"className":3210},[716],[574,3212,3214],{"className":3213},[630],[574,3215,3217],{"className":3216},[634],[574,3218,3220],{"className":3219,"style":2216},[638],[574,3221,3222,3225],{"style":2237},[574,3223],{"className":3224,"style":734},[645],[574,3226,3228],{"className":3227},[738,739,740,741],[574,3229,1022],{"className":3230},[625,741],[574,3232],{"className":3233,"style":972},[762],[574,3235,850],{"className":3236},[976],[574,3238],{"className":3239,"style":972},[762],[574,3241,3243,3246,3308,3311,3314],{"className":3242},[616],[574,3244],{"className":3245,"style":2800},[620],[574,3247,3249,3252,3305],{"className":3248},[625],[574,3250],{"className":3251},[878,1123],[574,3253,3255],{"className":3254},[1026],[574,3256,3258,3297],{"className":3257},[630,720],[574,3259,3261,3294],{"className":3260},[634],[574,3262,3264,3275,3283],{"className":3263,"style":2281},[638],[574,3265,3266,3269],{"style":2284},[574,3267],{"className":3268,"style":646},[645],[574,3270,3272],{"className":3271},[625],[574,3273,2615],{"className":3274},[625],[574,3276,3277,3280],{"style":1154},[574,3278],{"className":3279,"style":646},[645],[574,3281],{"className":3282,"style":1162},[1161],[574,3284,3285,3288],{"style":2304},[574,3286],{"className":3287,"style":646},[645],[574,3289,3291],{"className":3290},[625],[574,3292,3129],{"className":3293},[625],[574,3295,749],{"className":3296},[748],[574,3298,3300],{"className":3299},[634],[574,3301,3303],{"className":3302,"style":2323},[638],[574,3304],{},[574,3306],{"className":3307},[968,1123],[574,3309],{"className":3310,"style":972},[762],[574,3312,850],{"className":3313},[976],[574,3315],{"className":3316,"style":972},[762],[574,3318,3320,3324,3327,3333,3336,3339],{"className":3319},[616],[574,3321],{"className":3322,"style":3323},[620],"height:1.0663em;vertical-align:-0.1944em;",[574,3325,2963],{"className":3326},[625],[574,3328,3330],{"className":3329},[625],[574,3331,2950],{"className":3332},[2992],[574,3334,1022],{"className":3335},[625],[574,3337],{"className":3338,"style":1196},[762],[574,3340,3342,3349],{"className":3341},[625],[574,3343,3346],{"className":3344},[625,3345],"text",[574,3347,3187],{"className":3348},[625],[574,3350,3352],{"className":3351},[716],[574,3353,3355],{"className":3354},[630],[574,3356,3358],{"className":3357},[634],[574,3359,3362],{"className":3360,"style":3361},[638],"height:0.8719em;",[574,3363,3365,3368],{"style":3364},"top:-3.1208em;margin-right:0.05em;",[574,3366],{"className":3367,"style":734},[645],[574,3369,3371],{"className":3370},[738,739,740,741],[574,3372,1022],{"className":3373},[625,741],[565,3375,3376,3377,2130],{},"Mit dem Verschiebungssatz: ",[574,3378,3380,3441],{"className":3379},[577],[574,3381,3383],{"className":3382},[581],[583,3384,3385],{"xmlns":585},[587,3386,3387,3438],{},[590,3388,3389,3416,3418,3424,3426,3429,3431,3434,3436],{},[1026,3390,3391,3414],{},[590,3392,3393,3395,3397,3400,3402,3405,3407,3410,3412],{},[852,3394,3129],{},[601,3396,2720],{},[852,3398,3399],{},"49",[601,3401,2720],{},[852,3403,3404],{},"25",[601,3406,2720],{},[852,3408,3409],{},"81",[601,3411,2720],{},[852,3413,3404],{},[852,3415,2615],{},[601,3417,687],{},[1015,3419,3420,3422],{},[852,3421,2741],{},[852,3423,1022],{},[601,3425,850],{},[852,3427,3428],{},"39,2",[601,3430,687],{},[852,3432,3433],{},"36",[601,3435,850],{},[852,3437,3178],{},[605,3439,3440],{"encoding":607},"\\frac{16 + 49 + 25 + 81 + 25}{5} - 6^2 = 39{,}2 - 36 = 3{,}2",[574,3442,3444,3551,3595,3623,3641],{"className":3443,"ariaHidden":595},[612],[574,3445,3447,3450,3542,3545,3548],{"className":3446},[616],[574,3448],{"className":3449,"style":1116},[620],[574,3451,3453,3456,3539],{"className":3452},[625],[574,3454],{"className":3455},[878,1123],[574,3457,3459],{"className":3458},[1026],[574,3460,3462,3531],{"className":3461},[630,720],[574,3463,3465,3528],{"className":3464},[634],[574,3466,3468,3482,3490],{"className":3467,"style":1136},[638],[574,3469,3470,3473],{"style":1139},[574,3471],{"className":3472,"style":646},[645],[574,3474,3476],{"className":3475},[738,739,740,741],[574,3477,3479],{"className":3478},[625,741],[574,3480,2615],{"className":3481},[625,741],[574,3483,3484,3487],{"style":1154},[574,3485],{"className":3486,"style":646},[645],[574,3488],{"className":3489,"style":1162},[1161],[574,3491,3492,3495],{"style":1165},[574,3493],{"className":3494,"style":646},[645],[574,3496,3498],{"className":3497},[738,739,740,741],[574,3499,3501,3504,3507,3510,3513,3516,3519,3522,3525],{"className":3500},[625,741],[574,3502,3129],{"className":3503},[625,741],[574,3505,2720],{"className":3506},[767,741],[574,3508,3399],{"className":3509},[625,741],[574,3511,2720],{"className":3512},[767,741],[574,3514,3404],{"className":3515},[625,741],[574,3517,2720],{"className":3518},[767,741],[574,3520,3409],{"className":3521},[625,741],[574,3523,2720],{"className":3524},[767,741],[574,3526,3404],{"className":3527},[625,741],[574,3529,749],{"className":3530},[748],[574,3532,3534],{"className":3533},[634],[574,3535,3537],{"className":3536,"style":1187},[638],[574,3538],{},[574,3540],{"className":3541},[968,1123],[574,3543],{"className":3544,"style":763},[762],[574,3546,687],{"className":3547},[767],[574,3549],{"className":3550,"style":763},[762],[574,3552,3554,3557,3586,3589,3592],{"className":3553},[616],[574,3555],{"className":3556,"style":1070},[620],[574,3558,3560,3563],{"className":3559},[625],[574,3561,2741],{"className":3562},[625],[574,3564,3566],{"className":3565},[716],[574,3567,3569],{"className":3568},[630],[574,3570,3572],{"className":3571},[634],[574,3573,3575],{"className":3574,"style":1070},[638],[574,3576,3577,3580],{"style":1091},[574,3578],{"className":3579,"style":734},[645],[574,3581,3583],{"className":3582},[738,739,740,741],[574,3584,1022],{"className":3585},[625,741],[574,3587],{"className":3588,"style":972},[762],[574,3590,850],{"className":3591},[976],[574,3593],{"className":3594,"style":972},[762],[574,3596,3598,3601,3605,3611,3614,3617,3620],{"className":3597},[616],[574,3599],{"className":3600,"style":2982},[620],[574,3602,3604],{"className":3603},[625],"39",[574,3606,3608],{"className":3607},[625],[574,3609,2950],{"className":3610},[2992],[574,3612,1022],{"className":3613},[625],[574,3615],{"className":3616,"style":763},[762],[574,3618,687],{"className":3619},[767],[574,3621],{"className":3622,"style":763},[762],[574,3624,3626,3629,3632,3635,3638],{"className":3625},[616],[574,3627],{"className":3628,"style":986},[620],[574,3630,3433],{"className":3631},[625],[574,3633],{"className":3634,"style":972},[762],[574,3636,850],{"className":3637},[976],[574,3639],{"className":3640,"style":972},[762],[574,3642,3644,3647,3650,3656],{"className":3643},[616],[574,3645],{"className":3646,"style":2982},[620],[574,3648,2963],{"className":3649},[625],[574,3651,3653],{"className":3652},[625],[574,3654,2950],{"className":3655},[2992],[574,3657,1022],{"className":3658},[625],[565,3660,3661,3662,3736,3737,2130],{},"Als Stichprobenvarianz (Teilen durch ",[574,3663,3665,3687],{"className":3664},[577],[574,3666,3668],{"className":3667},[581],[583,3669,3670],{"xmlns":585},[587,3671,3672,3684],{},[590,3673,3674,3676,3678,3680,3682],{},[597,3675,1033],{},[601,3677,687],{},[852,3679,1030],{},[601,3681,850],{},[852,3683,2556],{},[605,3685,3686],{"encoding":607},"n - 1 = 4",[574,3688,3690,3709,3727],{"className":3689,"ariaHidden":595},[612],[574,3691,3693,3697,3700,3703,3706],{"className":3692},[616],[574,3694],{"className":3695,"style":3696},[620],"height:0.6667em;vertical-align:-0.0833em;",[574,3698,1033],{"className":3699},[625,650],[574,3701],{"className":3702,"style":763},[762],[574,3704,687],{"className":3705},[767],[574,3707],{"className":3708,"style":763},[762],[574,3710,3712,3715,3718,3721,3724],{"className":3711},[616],[574,3713],{"className":3714,"style":986},[620],[574,3716,1030],{"className":3717},[625],[574,3719],{"className":3720,"style":972},[762],[574,3722,850],{"className":3723},[976],[574,3725],{"className":3726,"style":972},[762],[574,3728,3730,3733],{"className":3729},[616],[574,3731],{"className":3732,"style":986},[620],[574,3734,2556],{"className":3735},[625],") ergäbe sich ",[574,3738,3740,3786],{"className":3739},[577],[574,3741,3743],{"className":3742},[581],[583,3744,3745],{"xmlns":585},[587,3746,3747,3783],{},[590,3748,3749,3763,3765,3771,3773,3775,3777],{},[1339,3750,3751,3753,3761],{},[597,3752,1019],{},[590,3754,3755,3757,3759],{},[597,3756,1033],{},[601,3758,687],{},[852,3760,1030],{},[852,3762,1022],{},[601,3764,850],{},[1026,3766,3767,3769],{},[852,3768,3129],{},[852,3770,2556],{},[601,3772,850],{},[852,3774,2556],{},[3180,3776,3182],{},[1015,3778,3779,3781],{},[3180,3780,3187],{},[852,3782,1022],{},[605,3784,3785],{"encoding":607},"s_{n-1}^2 = \\frac{16}{4} = 4\\,\\text{min}^2",[574,3787,3789,3864,3947],{"className":3788,"ariaHidden":595},[612],[574,3790,3792,3795,3855,3858,3861],{"className":3791},[616],[574,3793],{"className":3794,"style":1403},[620],[574,3796,3798,3801],{"className":3797},[625],[574,3799,1019],{"className":3800},[625,650],[574,3802,3804],{"className":3803},[716],[574,3805,3807,3847],{"className":3806},[630,720],[574,3808,3810,3844],{"className":3809},[634],[574,3811,3813,3833],{"className":3812,"style":1070},[638],[574,3814,3815,3818],{"style":1424},[574,3816],{"className":3817,"style":734},[645],[574,3819,3821],{"className":3820},[738,739,740,741],[574,3822,3824,3827,3830],{"className":3823},[625,741],[574,3825,1033],{"className":3826},[625,650,741],[574,3828,687],{"className":3829},[767,741],[574,3831,1030],{"className":3832},[625,741],[574,3834,3835,3838],{"style":1091},[574,3836],{"className":3837,"style":734},[645],[574,3839,3841],{"className":3840},[738,739,740,741],[574,3842,1022],{"className":3843},[625,741],[574,3845,749],{"className":3846},[748],[574,3848,3850],{"className":3849},[634],[574,3851,3853],{"className":3852,"style":1463},[638],[574,3854],{},[574,3856],{"className":3857,"style":972},[762],[574,3859,850],{"className":3860},[976],[574,3862],{"className":3863,"style":972},[762],[574,3865,3867,3870,3938,3941,3944],{"className":3866},[616],[574,3868],{"className":3869,"style":1116},[620],[574,3871,3873,3876,3935],{"className":3872},[625],[574,3874],{"className":3875},[878,1123],[574,3877,3879],{"className":3878},[1026],[574,3880,3882,3927],{"className":3881},[630,720],[574,3883,3885,3924],{"className":3884},[634],[574,3886,3888,3902,3910],{"className":3887,"style":1136},[638],[574,3889,3890,3893],{"style":1139},[574,3891],{"className":3892,"style":646},[645],[574,3894,3896],{"className":3895},[738,739,740,741],[574,3897,3899],{"className":3898},[625,741],[574,3900,2556],{"className":3901},[625,741],[574,3903,3904,3907],{"style":1154},[574,3905],{"className":3906,"style":646},[645],[574,3908],{"className":3909,"style":1162},[1161],[574,3911,3912,3915],{"style":1165},[574,3913],{"className":3914,"style":646},[645],[574,3916,3918],{"className":3917},[738,739,740,741],[574,3919,3921],{"className":3920},[625,741],[574,3922,3129],{"className":3923},[625,741],[574,3925,749],{"className":3926},[748],[574,3928,3930],{"className":3929},[634],[574,3931,3933],{"className":3932,"style":1187},[638],[574,3934],{},[574,3936],{"className":3937},[968,1123],[574,3939],{"className":3940,"style":972},[762],[574,3942,850],{"className":3943},[976],[574,3945],{"className":3946,"style":972},[762],[574,3948,3950,3953,3956,3959],{"className":3949},[616],[574,3951],{"className":3952,"style":3361},[620],[574,3954,2556],{"className":3955},[625],[574,3957],{"className":3958,"style":1196},[762],[574,3960,3962,3968],{"className":3961},[625],[574,3963,3965],{"className":3964},[625,3345],[574,3966,3187],{"className":3967},[625],[574,3969,3971],{"className":3970},[716],[574,3972,3974],{"className":3973},[630],[574,3975,3977],{"className":3976},[634],[574,3978,3980],{"className":3979,"style":3361},[638],[574,3981,3982,3985],{"style":3364},[574,3983],{"className":3984,"style":734},[645],[574,3986,3988],{"className":3987},[738,739,740,741],[574,3989,1022],{"className":3990},[625,741],[560,3992,3994],{"id":3993},"typische-fehler","Typische Fehler",[997,3996,3997,4028,4180,4183],{},[1000,3998,3999,4000,2130],{},"Die Abweichungen nicht quadrieren. Dann ist die Summe immer ",[574,4001,4003,4016],{"className":4002},[577],[574,4004,4006],{"className":4005},[581],[583,4007,4008],{"xmlns":585},[587,4009,4010,4014],{},[590,4011,4012],{},[852,4013,854],{},[605,4015,854],{"encoding":607},[574,4017,4019],{"className":4018,"ariaHidden":595},[612],[574,4020,4022,4025],{"className":4021},[616],[574,4023],{"className":4024,"style":986},[620],[574,4026,854],{"className":4027},[625],[1000,4029,4030,4031,4059,4060,4111,4112,4150,4151,4179],{},"Durch ",[574,4032,4034,4047],{"className":4033},[577],[574,4035,4037],{"className":4036},[581],[583,4038,4039],{"xmlns":585},[587,4040,4041,4045],{},[590,4042,4043],{},[597,4044,1033],{},[605,4046,1033],{"encoding":607},[574,4048,4050],{"className":4049,"ariaHidden":595},[612],[574,4051,4053,4056],{"className":4052},[616],[574,4054],{"className":4055,"style":1843},[620],[574,4057,1033],{"className":4058},[625,650]," oder ",[574,4061,4063,4081],{"className":4062},[577],[574,4064,4066],{"className":4065},[581],[583,4067,4068],{"xmlns":585},[587,4069,4070,4078],{},[590,4071,4072,4074,4076],{},[597,4073,1033],{},[601,4075,687],{},[852,4077,1030],{},[605,4079,4080],{"encoding":607},"n - 1",[574,4082,4084,4102],{"className":4083,"ariaHidden":595},[612],[574,4085,4087,4090,4093,4096,4099],{"className":4086},[616],[574,4088],{"className":4089,"style":3696},[620],[574,4091,1033],{"className":4092},[625,650],[574,4094],{"className":4095,"style":763},[762],[574,4097,687],{"className":4098},[767],[574,4100],{"className":4101,"style":763},[762],[574,4103,4105,4108],{"className":4104},[616],[574,4106],{"className":4107,"style":986},[620],[574,4109,1030],{"className":4110},[625]," teilen, ohne zu sagen, welche Variante gemeint ist. Bei kleinen Datensätzen unterscheiden sich die Ergebnisse deutlich (hier ",[574,4113,4115,4129],{"className":4114},[577],[574,4116,4118],{"className":4117},[581],[583,4119,4120],{"xmlns":585},[587,4121,4122,4126],{},[590,4123,4124],{},[852,4125,3178],{},[605,4127,4128],{"encoding":607},"3{,}2",[574,4130,4132],{"className":4131,"ariaHidden":595},[612],[574,4133,4135,4138,4141,4147],{"className":4134},[616],[574,4136],{"className":4137,"style":2982},[620],[574,4139,2963],{"className":4140},[625],[574,4142,4144],{"className":4143},[625],[574,4145,2950],{"className":4146},[2992],[574,4148,1022],{"className":4149},[625]," gegenüber ",[574,4152,4154,4167],{"className":4153},[577],[574,4155,4157],{"className":4156},[581],[583,4158,4159],{"xmlns":585},[587,4160,4161,4165],{},[590,4162,4163],{},[852,4164,2556],{},[605,4166,2556],{"encoding":607},[574,4168,4170],{"className":4169,"ariaHidden":595},[612],[574,4171,4173,4176],{"className":4172},[616],[574,4174],{"className":4175,"style":986},[620],[574,4177,2556],{"className":4178},[625],").",[1000,4181,4182],{},"Beim Verschiebungssatz die Reihenfolge vertauschen: Es heißt „Mittelwert der Quadrate minus Quadrat des Mittelwerts“, nicht umgekehrt. Das Ergebnis darf nie negativ sein.",[1000,4184,4185,4186,2130],{},"Die Varianz mit der Einheit der Daten angeben. Sie hat die quadrierte Einheit, hier ",[574,4187,4189,4207],{"className":4188},[577],[574,4190,4192],{"className":4191},[581],[583,4193,4194],{"xmlns":585},[587,4195,4196,4204],{},[590,4197,4198],{},[1015,4199,4200,4202],{},[3180,4201,3187],{},[852,4203,1022],{},[605,4205,4206],{"encoding":607},"\\text{min}^2",[574,4208,4210],{"className":4209,"ariaHidden":595},[612],[574,4211,4213,4216],{"className":4212},[616],[574,4214],{"className":4215,"style":3361},[620],[574,4217,4219,4225],{"className":4218},[625],[574,4220,4222],{"className":4221},[625,3345],[574,4223,3187],{"className":4224},[625],[574,4226,4228],{"className":4227},[716],[574,4229,4231],{"className":4230},[630],[574,4232,4234],{"className":4233},[634],[574,4235,4237],{"className":4236,"style":3361},[638],[574,4238,4239,4242],{"style":3364},[574,4240],{"className":4241,"style":734},[645],[574,4243,4245],{"className":4244},[738,739,740,741],[574,4246,1022],{"className":4247},[625,741],{"title":4249,"searchDepth":4250,"depth":4250,"links":4251},"",2,[4252,4253,4254],{"id":562,"depth":4250,"text":563},{"id":2537,"depth":4250,"text":2538},{"id":3993,"depth":4250,"text":3994},[4256,4259,4261,4263,4266,4268,4271],{"lhs":4257,"rhs":4258},"((a - (a+b+c)\u002F3)^2 + (b - (a+b+c)\u002F3)^2 + (c - (a+b+c)\u002F3)^2) \u002F 3","(a^2 + b^2 + c^2)\u002F3 - ((a+b+c)\u002F3)^2",{"lhs":4260,"rhs":2741},"(4 + 7 + 5 + 9 + 5) \u002F 5",{"lhs":4262,"rhs":3129},"(4-6)^2 + (7-6)^2 + (5-6)^2 + (9-6)^2 + (5-6)^2",{"lhs":4264,"rhs":4265},"16 \u002F 5","3.2",{"lhs":4267,"rhs":2556},"16 \u002F 4",{"lhs":4269,"rhs":4270},"(4^2 + 7^2 + 5^2 + 9^2 + 5^2) \u002F 5","39.2",{"lhs":4272,"rhs":4265},"39.2 - 6^2","n \\geq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","empirical-variance","s^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\bar{x})^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>s\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>ˉ\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\bar{x})^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2777em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1141em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.5678em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2222em;\">\u003Cspan class=\"mord\">ˉ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz",[],[4286,4287,4288],"arithmetic-mean","standard-deviation","expected-value",{"title":548,"description":4249},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz","Die empirische Varianz ist der Mittelwert der quadrierten Abweichungen der Daten von ihrem Mittelwert.",[4293,4294,4295,4296,4297],"varianz","streuung","statistik","stichprobe","mittelwert",[4299,4303,4306,4310,4313],{"symbol":4300,"meaning":4301,"symbolHtml":4302},"s^2","empirische Varianz der Daten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>s\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1033,"meaning":4304,"symbolHtml":4305},"Anzahl der Datenwerte","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4307,"meaning":4308,"symbolHtml":4309},"x_i","der i-te Datenwert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":684,"meaning":4311,"symbolHtml":4312},"Laufindex von 1 bis n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":608,"meaning":4314,"symbolHtml":4315},"arithmetisches Mittel der Daten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>ˉ\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\bar{x}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5678em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.5678em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2222em;\">\u003Cspan class=\"mord\">ˉ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","HnlBS1g042rYBQh2kfBjvysJl9S_fBZeZa6yqaEg51I",[4318,4321,4324],{"stem":4319,"title":4320,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Farithmetisches-mittel","Arithmetisches Mittel",{"stem":4322,"title":4323,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert","Erwartungswert",{"stem":4325,"title":4326,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstandardabweichung","Standardabweichung",1793824285113]