In a series of 2n observations, half of them equal to a and remaining half equal to -a . If standard

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13.Statistics

hard

In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals

$\frac{{\sqrt 2 }}{n}$

$\sqrt 2 $

$2$

$\frac{1}{n}$

(AIEEE-2004)

Solution

(c) Let $a, a, ……..n$ times and $-a, -a, -a, -a, ……..n$ times i.e., mean = $0$ and $S.D.$ $ = \sqrt {\frac{{n{{(a – 0)}^2} + n{{( – a – 0)}^2}}}{{2n}}} $

$2 = \sqrt {\frac{{n{a^2} + n{a^2}}}{{2n}}} = \sqrt {{a^2}} = \pm a$.

Hence $|a|\; = 2$.

Standard 11

Mathematics

Consider a set of $3 n$ numbers having variance $4.$ In this set, the mean of first $2 n$ numbers is $6$ and the mean of the remaining $n$ numbers is $3.$ A new set is constructed by adding $1$ into each of first $2 n$ numbers, and subtracting $1$ from each of the remaining $n$ numbers. If the variance of the new set is $k$, then $9 k$ is equal to …. .

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Find the mean and variance for the data

${x_i}$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

${f_i}$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

medium

${x_i}$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
${f_i}$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals

Solution

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Find the mean and variance for the data

${x_i}$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

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