The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is?

x̄ = Σxi/n = 9
s.d. = √Σ(xi - x̄)²/n = 0
⇒ xi = x̄ ∀i ∴ each term in the original observation is 9
⇒ observation = 9, 9, 9, 9, 9
x̄new = Σxi/n = 9 + 9 + 9 + 9 + x/5
⇒ 10 = 36 + x/5
⇒ x = 14
⇒ new set of observations = 9, 9, 9, 9, 14
s.dnew = √Σ(xi - x̄new)²/n = √(9 - 10)² + (9 - 10)² + (9 - 10)² + (9 - 10)² + (14 - 10)²/5 = √4 + 4 + 4 + 16/5 = √20/5 = 2