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The first of two groups of samples has 100 observations with mean 15 and Standard deviation(S.D) = 3, if the two groups together have 250 observations with mean 15.6 and S.D = $\sqrt{13.44}$ then S.D of second group is

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answer is A.

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Detailed Solution

We know that $σ^{2} = \frac{n_{1} (σ_{1}^{2} + d_{1}^{2}) + n_{2}^{2} (σ_{2}^{2} + d_{2}^{2})}{n_{1} + n_{2}}$

$d_{1} = m_{1} - a, d_{2} = m_{2} - a$

Where a is mean of whole group $15.6 = \frac{(100) (15) + (150) (m_{2})}{250}$

$m_{2} = 16$

$1.3.44 = \frac{((100 \times 9) + (150 \times σ^{2})) + ((100 \times {(0.6)}^{2}) + (150 \times {(0.4)}^{2}))}{250}$

$33.60 = 900 + 150 σ^{2} + 36 + 24$

$σ^{2} = 16 \Rightarrow σ = 4$

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