The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5 . Then, the correct variance is equal to _____.

Step-by-step solution

Old mean = x 1 + x 2 + . . . x 14 + 5 15 = 8 (given) ⇒ x 1 + x 2 + . . . x 14 = 115 Correct mean = x 1 + x 2 + . . . x 14 + 20 15 = x ¯ new ⇒ x ¯ new = 9 Given, old variance = 9 ⇒ x 1 2 + x 2 2 + . . . x 14 2 + 5 2 15 - 8 2 = 9 ⇒ x 1 2 + x 2 2 + . . . x 14 2 = 1070 Now var new = x 1 2 + x 2 2 + . . . x 14 2 + 20 2 15 - 9 2 = 1070 + 400 15 - 81 = 17