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Q.

A sample of 90 values has mean 55 and standard
deviation 3. A second sample of 110 values has mean
60 and standard deviation 2. The combined variance
is equal to (upto two decimal)

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a

12.43

b

11. 24

c

10.43

d

13.25

answer is A.

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Detailed Solution

$\begin{array}{l} n_{1} = 90, {\bar{x}}_{1} = 55, σ_{1} = 3, n_{2} = 110, {\bar{x}}_{2} = 60 and σ_{2} = 2 \\ {\bar{x}}^{2} = \frac{90 \times 55 + 110 \times 60}{200} = 57.75 \\ d_{1} = 55 - 57.75 = - 2.75 \\ d_{2} = 60 - 57.75 = 2.25 \\ σ^{2} = \frac{90 (9 + 7.5625) + 110 (4 + 5.0625)}{200} \\ = 12.43 (App) . \end{array}$

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A sample of 90 values has mean 55 and standarddeviation 3. A second sample of 110 values has mean60 and standard deviation 2. The combined varianceis equal to (upto two decimal)