The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38 σ 2 is equal to _______.

Step-by-step solution

Given, Wrong mean = μ 1 = 30 Wrong standard deviation = σ 1 = 5 Now mean ig given by ∑ x i 40 = 30 ⇒ ∑ x i = 1200 Variance is given by σ 1 2 = 25 ⇒ ∑ x i 2 40 - 30 2 = 25 ⇒ ∑ x i 2 = 925 × 40 = 37000 New sum of mean = ∑ x i ' = 1200 - 10 - 12 = 1178 So, new mean = μ 1 ' = 1178 38 = 31 Now new variance ∑ x i 2 = 37000 - 10 2 - 12 2 = 36756 So, new S.D. σ 1 ' = 36756 38 - 31 2 = σ 36756 - 31 2 × 38 = 38 σ 2