Question

if the sum of the deviations of a set of values x1 x2 x3 ...........xn measured from 50 is -10 and the sum of deviations of the values from 46 is 70 then find its mean

Answer 1

Solution :-

The deviation X1, X2, ..........Xn from 50 are (X1 - 50), (X2 - 50), ......(Xn - 50)

Hence, the sum is

(X1 - 50) + (X2 - 50) + ..........(Xn - 50) = - 10

(X1 + X2 + ......Xn) - 50n = - 10 ............(1)

Similarly, we have

(X1 + X2 +..........Xn) - 46n = 70 ............(2)

Subtracting equation (2) from (1), we get.

⇒ (X1 + X2 +.........Xn) - 50n = - 10
    (X1 + X2 +.........Xn) - 46n = 70
                                     +          -
____________________________
                                    - 4n = - 80                        
____________________________

⇒ - 4n = - 80

⇒ 4n = 80         

⇒ n = 80/4

⇒ n = 20

Substituting the value of n = 20 in (1)

(X1 + X2 +...........Xn) - 50*20 = - 10

(X1 + X2 +...........Xn) - 1000 = - 10

(X1 + X2 +...........Xn) = 1000 - 10

(X1 + X2 +...........Xn) = 990

Hence, the mean = (X1 + X2 +.........Xn)/n

⇒ 990/20

Mean = 49.5 

Answer.