In a set of 2 n observations, half of them are equal to ' α ' and the remaining half are equal to ' -α '. If the standard deviation of all the observations is 2 , then the value of |α| is equal to

Question

In a set of 2 n observations, half of them are equal to ' α ' and the remaining half are equal to ' -α '. If the standard deviation of all the observations is 2 , then the value of |α| is equal to (A) 2 (B) √2 (C) 2 √2 (D) 4

Tardigrade Admin · Accepted Answer

μ( mean )=0 Standard deviation =√( displaystyle∑i=12 n(xi-μ)2/2 n) ⇒|α|=2

Q. In a set of $2 n$ observations, half of them are equal to ' $α$ ' and the remaining half are equal to ' $- α$ '. If the standard deviation of all the observations is 2 , then the value of $∣ α ∣$ is equal to

2

$2$

$22$

4

$μ ($ mean $) = 0$
Standard deviation $= \frac{i = 1 \sum 2 n ( x _{i} - μ ) ^{2}}{2 n} \Rightarrow ∣ α ∣ = 2$

Q. In a set of 2n observations, half of them are equal to ' α ' and the remaining half are equal to ' −α '. If the standard deviation of all the observations is 2 , then the value of ∣α∣ is equal to

2

2​

22​

4

μ( mean )=0 Standard deviation =2ni=1∑2n​(xi​−μ)2​​⇒∣α∣=2

Q. In a set of $2 n$ observations, half of them are equal to ' $α$ ' and the remaining half are equal to ' $- α$ '. If the standard deviation of all the observations is 2 , then the value of $∣ α ∣$ is equal to

$2$

$22$

$μ ($ mean $) = 0$
Standard deviation $= \frac{i = 1 \sum 2 n ( x _{i} - μ ) ^{2}}{2 n} \Rightarrow ∣ α ∣ = 2$