JEE Main · 2010 · 11 Apr 2010 · Offline · Statistics

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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

(A) $\frac{11}{2}$ ✓ Correct
(B)6
(C) $\frac{13}{2}$
(D) $\frac{5}{2}$

Answer: (A)

Solution

With five numbers of mean

2

\sum x = 10

, and variance

4

gives

\frac{\sum x ^{2}}{5} - 2^{2} = 4

, so

\sum x^{2} = 40

. Likewise mean

4

gives

\sum y = 20

, and variance

5

gives

\frac{\sum y ^{2}}{5} - 4^{2} = 5

, so

\sum y^{2} = 105

. Combining the ten values, the mean is

\frac{10 + 20}{10} = 3

, and the variance is

\frac{\sum x ^{2} + \sum y ^{2}}{10} - 3^{2} = \frac{40 + 105}{10} - 9 = \frac{145}{10} - 9 = \frac{11}{2}

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option

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