The mean of `25` observation is `36.` Out of these observations, if the mean of first `13` observations is `32` and that of the last `13` observations is `40,` the `13th ` observation is

Options

A. `33`
B. `38`
C. `36 `
D. `46`

Answer

C

Explanation

Mean of `25` observations =` (36xx 25) =900`
Sum of `25` observations = `(36 xx 25) =900`
Mean of first `13` observations `= 32.`
Sum of first `13` observations `= (32 xx 13) = 416`
Mean of last `13` observations `= 40`
Sum of last `13` observations =` ( 40xx 13) = 520`
13th observation
= ( sum of first `13` observations) + ( sum of last `13` observations) - ( sum of `25` observations )
` = ( 416 + 520) -(900) = 936 -900 = 36 `