Find the mean deviation about the median for the data
x_i 5 7 9 10 12 15
f_i 8 6 2 2 2 6

Solution:

The given observations are in ascending order.

Adding a column corresponding to cumulative frequencies of the given data,

we obtain the following table.

Here, N = 26, which is even.

Hence,

Median is the mean of 13th and 14th observations.

Both the observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

M = [13^th observation + 14^th observation]/2

= (7 + 7)/2 = 7

The absolute values of the deviations, |x_i - M| are

⁶∑_{i = 1} f_i = 26 and ⁶∑_{i = 1} f_i|x_i - M| = 84

Hence, the mean deviation about the median

M.D.(M) = ⁶∑_{i = 1} f_i|x_i - M|

= 1/26 × 84

= 3.23

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 7

Find the mean deviation about the median for the data xi 5 7 9 10 12 15 fi 8 6 2 2 2 6

Summary:

The mean deviation about the median for the given data is 3.23