The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is 10 . 2 . then their new variance is equal to:

Step-by-step solution

Let the number of observations of the data set is n . So, ∑ x i = 10 n       . . . . i Also, ∑ x i - 8 + 12 = 10 . 2 n ⇒ 10 n + 4 = 10 . 2 n ⇒ 0 . 2 n = 4 ⇒ n = 20 Also, σ 2 = 4 = ∑ x i 2 20 - 100 ⇒ ∑ x i 2 = 104 × 20 = 2080 Now, new variance is = ∑ x i 2 - 8 2 + 12 2 20 - 10 . 2 2 = 2080 + 4 × 20 20 - 104 . 04 = 108 - 104 . 04 = 3 . 96