Question
Tue September 11, 2012 By:
 

The sum of 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. Find the values of n and the mean.

Expert Reply
Wed September 12, 2012

Sum of the deviations x1, x2, x3, … xn from 50 is -10.

So, (x1 - 50) + (x2 - 50) + (x3 - 50) … + (xn - 50) = -10

Or x1 + x2 + x3 …+ xn - 50n = -10

Or x1 + x2 + x3 …+ xn = 50n - 10                               … (1)

 

Sum of deviations of the values from 46 is 70

So, (x1 - 46) + (x2 - 46) + (x3 - 46) … + (xn - 46) = 70

Or x1 + x2 + x3 …+ xn - 46n = 70

Or 50n - 10 - 46n = 70                                  [Using (1)]

Or 4n = 80

Or n = 20

That is total number of observations is 20.

 

So, sum of observations = x1 + x2 + x3 …+ xn = 50 × 20 - 10 = 990

And hence, mean of the data is 990/20 = 49.5

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