Let $ x_{1}, x_{2}, \ldots \ldots \ldots \ldots x_{100} $ are $ 100 $ observations such that $ \sum x_{i}=0, \sum_{1 \leq i

Question

Let $ x_{1}, x_{2}, \ldots \ldots \ldots \ldots x_{100} $ are $ 100 $ observations such that $ \sum x_{i}=0, \sum_{1 \leq i < j \leq 100}\left|x_{i} x_{j}\right|=80000 \& $ mean deviation from their mean is $ 5 $, then their standard deviation is,

MARKS App · Accepted Answer

x - = ∑ x i 100 = 0 & ∑ x i - x - 100 = 5 ⇒ ∑ x i = 500 ⇒ ∑ x i 2 + 2 ∑ 1 ≤ i j ≤ 100 x i x j = 500 2 ⇒ ∑ x i 2 100 = 500 2 - 2 ∑ x i x j 100 = 2500 - 1600 S . D . = ∑ x i - x - 2 100 = 900 = 30

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