Let the mean and variance of 12 observations be 9 2 and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is m n , where m and n are coprime, then m + n are coprime, then m + n is equal to

Step-by-step solution

Given, The mean and variance of 12 observations be 9 2 and 4 respectively, So, mean will be, x ¯ = x 1 + x 2 + … … + 9 + 10 + … . . + x 12 12 = 9 2 ⇒ x 1 + x 2 … … + x 12 + 19 = 54 Now removing the observation 9   &   10 and adding the observation 7   &   14 , So, the new total sum of the observation will be, x 1 + x 2 + … … + x 12 + 7 + 14 = 54 - 19 + 7 + 14 Now new mean will be, x 1 + x 2 + … . + x 12 + 7 + 14 12 = 56 12 &#8658