Find the mean deviation about the mean for the data
x_i   10   30   50   70   90
f_i     4    24   28   16   8

Solution:

Let us make the table of the given data.

N = ⁵∑_{i = 1} f_i = 80 and ⁵∑_{i = 1} f_ix_i = 4000

Therefore,

x = 1/N ⁵∑_{i = 1} f_ix_i

= (1/80) × 4000

= 50

Mean deviation about the mean

M.D. (x) = ⁸∑_{i = 1} (|x_i - x|)/8

= 1/80 × 1280

= 16

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 6

Find the mean deviation about the mean for the data xi   10   30   50   70   90 fi     4    24   28   16   8

Summary:

The mean deviation about the mean for the given data is 16