The mean and standard deviation of 100 observations are 40 and 5.1 , respectively, By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are μ

Question

The mean and standard deviation of 100 observations are 40 and 5.1 , respectively, By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are μ and σ respectively, then 10 ( μ + σ ) is equal to

TestHub · Accepted Answer

​ Actual means = μ = 100 100 ( 40 ) − 50 + 40 ​ μ = 40 − 10 1 ​ = 39.9 ​ Incorrect variance ​ ( 5.1 ) 2 = 100 ∑ x i 2 ​ ​ − ( x ) 2 ∑ x i 2 ​ = 100 × ( 4 0 2 ) + 100 ( 5.1 ) 2 ∑ x i 2 ​ = 16 × 1 0 4 + ( 5.1 ) 2 × 100 = 162601 σ 2 = 100 ∑ x i 2 ​ − 5 0 2 + 4 0 2 ​ − ( μ ) 2 σ 2 = 1617.01 − ( 39.9 ) 2 = 25 σ = 5 10 ( μ + σ ) = 10 ( 39.9 + 5 ) = 10 × 44.9 = 449 ​

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