JEE MATHEMATICS MCQ: STATISTICS

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The first of two samples in a group 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 the standard deviation of the second sample is

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Correct option: C

Option C (4) is correct because it is the standard deviation calculated using the combined mean and standard deviation formulas, accounting for both samples.

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If the mean of a set of observations

{x_1},{x_2}, \ldots ,{x_n}

\bar X,

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{x_i} + 2\;i;i = 1,\;2, \ldots ,n

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the s.d. of the new set of observations will be