The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _______.

Step-by-step solution

Given, n = 10 and mean x ¯ = ∑ x i 10 = 15 ⇒ ∑ i = 1 10 x i = 150 ⇒ ∑ i = 1 9 x i + 25 = 150 ⇒ ∑ i = 1 9 x i = 125 Now new sum will be ∑ i = 1 9 x i + 15 = 140 So, actual mean = 140 10 = 14 = x ¯ new   Now finding variance ∑ x i 2 10 - x ¯ 2 = 15 ⇒ ∑ x i 2 10 - 15 2 = 15 ⇒ ∑ i = 1 10 x i 2 = 2400 Removing observation of 25 we get, ⇒ ∑ i = 1 9 x i 2 + 625 = 2400 ⇒ ∑ i = 1 9 x i 2 = 1775 Now addin