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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