Q7 of 33 Page 156

Find the sum of deviations of all observations of the data 5, 8, 10, 15, 22 from their mean.

Given, observations 5, 8, 10, 15, 22

Clearly, No of observations, n = 5


We know,


Arithmetic mean of x1, x2, x3, …, xn (n observations) is



Therefore, mean of above data




Hence, mean is 12


Now, we know deviation


di = xi - a


in this case, a = 12


d1 = x1 - a = 5 - 12 = -7


d2 = x2 - a = 8 - 12 = -4


d3 = x3 - a = 10 - 12 = -2


d4 = x4 - a = 15 - 12 = 3


d5 = x5 - a = 22 - 12 = 10


Sum of deviations = (-7) + (-4) + (-2) + 3 + 10 = 0


Hence, sum of deviations from their mean is 0.


More from this chapter

All 33 →
5

Five years ago mean age of a family was 25 years. What is the present mean age of the family?

 6

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.

 8

If sum of the 20 deviations from the mean is 100, then find the mean deviation.

 9

Marks of 12 students in a unit test are given as 4, 21, 13, 17, 5, 9, 10, 20, 19, 12, 20, 14.

Assume a mean and calculate the arithmetic mean of the data. Assume another number as mean and calculate the arithmetic mean again. Do you get the same result? Comment.