Question

12. Find the mean deviation about the median for the following data :
(i) Class interval 0-6 6-12 12-18 18 - 24 24-30
Frequency
4
5
3
6
2
5

Answer 1

Given:

Class interval and frequency have been given in the question.

To find:

We have to find the mean deviation about the median for the following data.

Solution:

We need to draw the table to understand the solution completely.

Class     Frequency

interval      $f_{i}$                $x_{i}$             c.f            ∣$x_{i}$   − 14∣       $f_{i}$∣ $x_{i}$ − 14∣

0-6            4                 3                4                 11                    44

6-12           5                 9                9                 5                   25

12-18          3                 15               12                1                     3

18-24          6                21                18               7                   42

24-30         2                27               20              13                  26

              N = 20                                                              $\sum$ $f_i$ ∣ $x_{i}$ − 14∣  = 140  

We can see that,  N = 20

∴N/2 = 20/2 = 10

We can see N/2 = 10 which lies in the interval 12 - 18.

Thus 12 - 18 will be the median class.

Now, L = 12, h = 6 and F = 9, where

L = lower limit of median class

h = height of median class

f = Frequency of median class

By using the formula

∴ Median = L + $\frac{N/2-c.f}{f}$ ×h[c.f is cumulative frequency of preceding class]

                = 12 + $\frac{10 - 9}{3}$ × 6

                = 12 + $\frac{1}{3}$ × 6

                = 12 + 2 = 14

Now we have to find the value of mean deviation:

Mean deviation about median = $\frac{\sum f_i | x_i - x|}{\sum f_i}$

                                                    = $\frac{140}{20}$ = 7

Therefore, the mean deviation about the median for the given data is 7.