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Question:

A data consists of n observation: x1, x2, ..., xn. If Σᵢ₌₁ⁿ(xi + 1)² = 9n and Σᵢ₌₁ⁿ(xi - 1)² = 5n, then the standard deviation of this data is:

√5

√7

2

5

Solution:

The correct option is B
√5
Σ(xi+1)²=9n.. (1)
Σ(xi-1)²=5n. (2)
(1)+(2) ⇒ Σ(x²i+1)=7n ⇒ Σx²i=6n
(1)-(2) ⇒ 4Σxi=4n ⇒ Σxi=n ⇒mean=1
variance=6-1=5
⇒Standard deviation=√5