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JEE MATHEMATICS MCQ: STATISTICS

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The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and

\sigma^{2}

respectively. If the variance of all the 30 numbers in the two sets is 13 , then

\sigma^{2}

is equal to

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Correct option: A

10

Option A (10) is correct because it is the variance of the second set of numbers, calculated using the combined variance formula.

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\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