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The mean and standard deviation of 50 observations are 50 and 10 . Later on, it was decided to omit an observation that was incorrectly recorded as 99 . If the variance of the remaining 49 observations is λ 49 , then the value of λ is equal to

Correct answer

2550

Step-by-step solution

x - = ∑ x 1 50 = 50 ⇒ ∑ x i = 2500 Correct ∑ x i = 2500 - 99 = 2401 Correct x - = 2401 49 = 49 σ 2 = ∑ x i 2 n - x - 2 ⇒ 100 = ∑ x i 2 50 - 2500 ⇒ ∑ x i 2 = 130000 Correct ∑ x i 2 = 130000 - 99 2 = 120199 Correct σ 2 = ∑ x i 2 n - x - 2 = 120199 49 - 49 2 = 120199 - 117649 49 = 2550 49 = λ 49 Hence, λ = 2550

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