Find the mean deviation about the median for the data
x_i   15   21   27   30   35
f_i     3    5     6      7     8

Solution:

The given observations are in ascending order.

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

we obtain the following table.

xi	fi	c. f
15	3	3
21	5	8
27	6	14
30	7	21
35	8	29

Here, N = 29, which is odd.

Median = (29 + 1)/2 = 15^th observation

This observation lies in the cumulative frequency 21, for which the corresponding observation is 30.

Therefore,

Median = 30

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

|xi - M|	15	9	3	0	5
fi	3	5	6	7	8
|fi xi - M|	45	45	18	0	40

Here, ⁵∑_{i = 1} f_i = 29 and ⁵∑_{i = 1} f_i|x_i - M| = 148

M.D.(M) = ⁵∑_{i = 1} f_i|x_i - M|

= 1/29 × 148

= 5.1

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 Question 8

Find the mean deviation about the median for the data xi   15   21   27   30   35 fi     3    5     6      7     8

Summary:

The mean deviation about the median for the given data is 5.1