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The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean $15.6$ and standard deviation $\sqrt{13.44},$ then which of the following option(s) is/are true?

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the mean of the second group is 16

the standard deviation of the second group is 4

the mean of the second group is 4

the standard deviation of the second group is 2

answer is A, B.

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Detailed Solution

Use $σ^{2} = \frac{n_{1} {σ_{1}}^{2} + n_{2} {σ_{2}}^{2}}{n_{1} + n_{2}} + \frac{n_{1} n_{2}}{{(n_{1} + n_{2})}^{2}} {({\bar{x}}_{1} - {\bar{x}}_{2})}^{2}$

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