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 vari - Mathematics MCQ AIEEE 2026 | ExamTest.live | ExamTest.live

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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 $11/2$
B $6$
C $13/2$
D $5/2$

Solution & Step-by-step Explanation

Formula for combined variance σ^{2} : σ^{2} = \frac{n _{1} ( σ _{1}^{2} + d _{1}^{2} ) + n _{2} ( σ _{2}^{2} + d _{2}^{2} )}{n _{1} + n _{2}} where d_{1} = \overset{x}{ˉ}_{1} - \overset{ˉ}{X}, d_{2} = \overset{x}{ˉ}_{2} - \overset{ˉ}{X}, and \overset{ˉ}{X} is combined mean. \overset{ˉ}{X} = \frac{5 ( 2 ) + 5 ( 4 )}{10} = 3 . d_{1} = 2 - 3 = - 1 ⟹ d_{1}^{2} = 1 . d_{2} = 4 - 3 = 1 ⟹ d_{2}^{2} = 1 . σ^{2} = \frac{5 ( 4 + 1 ) + 5 ( 5 + 1 )}{10} = \frac{5 ( 5 ) + 5 ( 6 )}{10} = \frac{25 + 30}{10} = \frac{55}{10} = 5.5 = 11/2 .

Practice this question

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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

11/2

B

6

C

13/2

D

5/2

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