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JEE MATHEMATICS MCQ: STATISTICS

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Application +4 | -1

If

{\bar x}

is the arithmetic mean of n independent variates

{x_1},{x_2},{x_3}, \ldots ,{x_n}

each of the standard derivation σ, then variance

\left( {\bar x} \right)

is

View answer and explanation

Correct option: A

\frac{{{\sigma ^2}}}{n}

Option A (

\frac{{\sigma ^2}}{n}

) is correct because the variance of the mean of n independent variates is the variance of the individual variates divided by n.

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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

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-2,

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