The mean and standard deviation of 20 observations were calculated as 10 and 2 . 5 respectively. It was found that by mistake one data value was taken as 25 instead of 35 . If α and β are the mean and standard deviation respectively for correct data, then ( α , β ) is:

Step-by-step solution

Mean = x 1 + x 2 + x 3 + … … + x 19 + 25 20 = 10 ⇒ x 1 + x 2 + x 3 + … … … + x 19 + 25 = 200 ⇒ x 1 + x 2 + x 3 + … … … + x 19 = 175 New mean = x 1 + x 2 + x 3 + … … + x 19 + 35 20 = 175 + 35 20 = 10 . 5 S.D. = x 1 2 + x 2 2 + x 3 2 + … … + x 19 2 + ( 25 ) 2 20 - ( 10 ) 2 ⇒ 2 . 5 = x 1 2 + x 2 2 + x 3 2 + … … + x 19 2 + ( 25 ) 2 20 - ( 10 ) 2 ⇒ x 1 2 + x 2 2 + x 3 2 + … … + x 19 2 = 1500 New