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.
Rate this question :






















If the mean of a set of observations x1, x2, ...., ...., x10 is 20. Find the mean of x1 + 4, x2 + 8, x3 + 12, .... ...., x10 + 40.
AP - MathematicsMean of eight observations is 25. If one observation 11 is excluded, find the mean of the remaining.
AP - MathematicsFind the mean of the data;10.25, 9, 4.75, 8, 2.65, 12, 2.35
AP - MathematicsFive years ago mean age of a family was 25 years. What is the present mean age of the family?
AP - Mathematics