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

Question

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

TestHub · Accepted Answer

Clearly mean A = 0 Now, standard deviation σ = 2 n Σ ( x − A ) 2 ​ ​ 2 = ​ 2 n ( a − 0 ) 2 + ( a − 0 ) 2 + …… + ( 0 − a ) 2 + … .. ​ ​ = 2 n a 2 ⋅ 2 n ​ ​ = ∣ a ∣ ​ Hence, ∣ a ∣ = 2

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