Question

If the sum of deviations of a set of values x1 x2 x3 xn measured from 59 is - 20 and from 44 is 70 then the sample size and and the sample mean as

Answer 1

Answer

The deviations of 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) - 50 n = -10 ...(1)

similarly we have

(x1 + x2 + .....xn) - 46n = 70 ...(2)

equation (2) - (1) gives

-4n = -80

n = 20

substituting the value of n in (1)

(x1 + x2 + ....xn) - 50 (20) = -10

(x1 + x2 + ....xn) = 990

Hence the mean

(x1 + x2 + ....xn) /n = 990/20 = 49.5

Hope This helps :)