If the mean and variance of five observations are 24 5 and 194 25 respectively and the mean of first four observations is 7 2 , then the variance of the first four observations in equal to

Step-by-step solution

Given: x = 24 5 and variance is 194 25 ⇒ ∑ i = 1 5 x i = 24 5 × 5 ⇒ ∑ i = 1 5 x i = 24 Also, variance ⇒ ∑ i = 1 5 x i 2 5 - 24 5 2 = 194 25 ⇒ ∑ i = 1 5 x i 2 = 154 Now, 5 th observation = 24 - sum of first 4 terms = 24 - 7 2 × 4 = 10 So, new variance = ∑ i = 1 4 x i 2 4 - 7 2 2 = 154 - 100 4 - 49 4 = 5 4