JEE MATHEMATICS MCQ: STATISTICS

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Application +4 | -1

The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively, their standard deviations were 3 and 4 respectively the variance of combined sample size of 500 is

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Correct option: C

67.2

Option C (67.2) is correct because the combined variance is calculated using the formula

\sigma^{2} = \frac{{n_{{1}}(\sigma_{{1}}^{{2}}+d_{{1}}^{{2}})+n_{{2}}(\sigma_{{2}}^{{2}}+d_{{2}}^{{2}})}}{{n_{{1}}+n_{{2}}}}

, where

d_i

is the difference between the individual mean and the combined mean.

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If the mean of a set of observations

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

\bar X,

then the mean of the observations

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

is The sum of 10 items is 12 and sum of their squares is 18 , then standard deviation will be In a family, there are 8 men, 7 women and 5 children whose mean ages separately are respectively 24,20 and 6 years. The mean age of the family is The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is

1,3,5, x, y

are 5 observations. Mean of these observations is 5 and variance is 8. Sum of the cubes of the two missing number equals: If s.d. of a set of observations is 8 and if each observation is divided by

-2,

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