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The mean square deviation of a set of observations x 1 , x 2 . . . . . . x n about a point m is defined as 1 n ∑ i = 1 n x i - m 2 . If the mean square deviations about – 1 and 1 of a set of observations are 7 and 3 respectively. The standard deviation of those observations is

Options

  1. A2
  2. B2
  3. C5
  4. D3

Correct answer

D. 3

Step-by-step solution

∑ i = 1 n x i + 1 2 n = 7 (given) ⇒ ∑ x i 2 + 2 ∑ x i + n = 7 n ⇒ ∑ x i 2 + 2 ∑ x i = 6 n … (1) Also, ∑ x i - 1 2 n = 2 (given) ⇒ ∑ x i 2 - 2 ∑ x i + n = 3 n ⇒ ∑ x i 2 - 2 ∑ x i = 2 n … (2) From ( 1 ) and ( 2 ) ∑ x i 2 = 4 n ,   ∑ x i = n Standard deviation = ∑ x i 2 n - ∑ x i n 2 = 4 n n - 1 = 3

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