For two data sets, each of size 5, the variances are given

Question

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is -

Latika Leekha · Accepted Answer

The size of each data set is 5 i.e. N = 5.Let M1 and M2 denote the means of the two data sets.Let V1 and V2 be the variance.Then, we have V1 = 4 which means 1/5 &Sigma; xi2 &ndash; 22 = 4Hence, 1/5 &Sigma; xi2 = 16 which gives &Sigma; xi2 = 40.Also, we have V2 = 5 which means 1/5 &Sigma; yi2 &ndash; 42 = 5Hence, 1/5 &Sigma; yi2 = 21 which gives &Sigma; yi2 = 105.Hence, we have &Sigma; ( xi2 + yi2 ) = 145Also &Sigma; xi = N .M1 = 5. 2 = 10Similarly, &Sigma; yi = N .M2 = 5. 4 = 20So, &Sigma; (xi + yi) = 10+20 = 30.Variance of the combined data set = 1/10 &Sigma; ( xi2 + yi2 ) &ndash; (1/10 &Sigma; (xi + yi) )2 = 145/10 &ndash; 9 = 55/10 = 11/2.Thanks & RegardsLatika LeekhaaskIITians Faculty

Algebra> For two data sets, each of size 5, the va...

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is -

saket kumar , 12 Years ago

Latika Leekha

ASh

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Algebra> For two data sets, each of size 5, the va...

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is -

saket kumar , 12 Years ago

Latika Leekha

ASh

LIVE ONLINE CLASSES

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