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The mean and the standard deviation S . D . of five observations are 9 and 0 , respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10 , then their S . D . is

Options

  1. A0
  2. B2
  3. C4
  4. D1

Correct answer

B. 2

Step-by-step solution

x ¯ = ∑ x i n = 9 s . d = ∑ x i - x ¯ 2 n = 0 ⇒ x i = x ¯ ∀ i ∴ each term in the original observation is 9 ⇒ observation 1 = 9 , 9 , 9 , 9 , 9 x ¯ new   = ∑ x i n = 9 + 9 + 9 + 9 + x 5 5 ⇒ 10 = 36 + x 5 5 ⇒ x 5 = 14 ⇒ new set of observations = 9 , 9 , 9 , 9 , 14 s . d new   = ∑ x i - x ¯ new 2 n = ( 9 - 10 ) 2 + ( 9 - 10 ) 2 + ( 9 - 10 ) 2 + ( 14 - 10 ) 2 5 = 4 + 4 2 5 = 20 5 = 2

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