Q. 114.4( 60 Votes )

The sum of deviations of ‘n’ observations from 25 is 25 and sum of deviations of the same ‘n’ observations from 35 is − 25. Find the mean of the observations.

Answer :

Given, no of observations = n

And sum of deviation from 25 is 25 and sum of deviation from 35 is -25.


Let the actual mean be x,


We know that


Arithmetic mean,


Where, a is assumed mean.


In first case, where assumed mean, a = 25 and sum of deviation is 25, Putting values in formula


We have,


[1]


In first case, where assumed mean, a = 35 and sum of deviation is -25, Putting values in formula


We have,


[2]


Adding [1] and [2], we get



2x = 60


x = 30


arithmetic mean of required data is 30.


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