NTA Abhyas JEE Main2020MathematicsStatisticsPractice

In a series of 2 n observations, half of them are equal to a 2 and the remaining half are equal to – a 2 . If the standard deviation of the observations is 2 , then a is equal to

Options

A1 n
B2
C2
D2 n

Correct answer

B. 2

Step-by-step solution

x i = a 2 for i = 1,2 ,. . , n and x i = - a 2 for i = n + 1 ,... 2 n S . D = 1 2 n ∑ i = 1 2 n x i - x - 2 ⇒ 2 = 1 2 n ∑ i = 1 2 n x i 2 S i n c e ∑ i = 1 2 n x i = 0 ⇒ 2 = 1 2 n ⋅ 2 n a 4 ⇒ a = 2

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