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

Q. Let in a series

2 n

observations, half of them are equal to

a

and remaining half are equal to

- a

. Also by adding a constant

b

in each of these observations, the mean and standard deviation of new set become

5

20

, respectively. Then the value of

a^{2} + b^{2}

is equal to

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In a series of 2n observations, half of them equal a and remaining half equal -a. If the S.D of the observations is 2 then |a| =___

The correct option is C 2Meanμ=0 SD=σ=√∑(x−μ)22n⇒√(a−0)2+(a−0)2+⋯⋯⋯+(a−0)22n=2 ⇒√a2.2n2n=2⇒|a|=2

The correct option is C $2$
$M e a n μ = 0$
$S D = σ = \sqrt{\frac{\sum (x - μ)^{2}}{2 n}} \Rightarrow \sqrt{\frac{(a - 0)^{2} + (a - 0)^{2} + \dots \dots \dots + (a - 0)^{2}}{2 n}} = 2$
$\Rightarrow \sqrt{\frac{a^{2} .2 n}{2 n}} = 2 \Rightarrow | a | = 2$