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.
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
Where, a is assumed mean.
In first case, where assumed mean, a = 25 and sum of deviation is 25, Putting values in formula
In first case, where assumed mean, a = 35 and sum of deviation is -25, Putting values in formula
Adding  and , we get
⇒ 2x = 60
⇒ x = 30
⇒ arithmetic mean of required data is 30.
Rate this question :
Find the arithmetic mean of the sales per day in a fair price shop in a week.
Rs. 10000, Rs. .10250, Rs. .10790, Rs. .9865, Rs. .15350, Rs. .10110AP - Mathematics
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 - Mathematics
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.AP - Mathematics
Mean of eight observations is 25. If one observation 11 is excluded, find the mean of the remaining.AP - Mathematics
Find the mean of the data;10.25, 9, 4.75, 8, 2.65, 12, 2.35AP - Mathematics
Five years ago mean age of a family was 25 years. What is the present mean age of the family?AP - Mathematics
Arithmetic mean of nine observations is calculated as 38. But in doing so, an observation 27 is mistaken for 72. Find the actual mean of the data.AP - Mathematics
Two years ago the mean age of 40 people was 11 years. Now a person left the group and the mean age is changed to 12 years. Find the age of the person who left the group.AP - Mathematics
Find the sum of deviations of all observations of the data 5, 8, 10, 15, 22 from their mean.AP - Mathematics