Find the mean deviation about the median from the following data. | Statistics | SciPiPupil

Question: Find the mean deviation about the median for the following data.

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	6	7	15	16	4	2

Solution:

Arranging given data in cumulative frequency (c.f.) table,

Class	Frequency	c.f.
0-10	6	6
10-20	7	13
20-30	15	28
30-40	16	44
40-50	4	48
50-60	2	50
	N=50

Median (M) class = $\dfrac{N}{2}^{th} class$

$= \dfrac{50}{2}^{th} class$

$= 25^{th} class$

In c.f. table, just greater value than 25 is 28 whose corresponding class is (20-30). So, median class = (20-30).

So we know,

l = 20, i = 10, f = 15, c.f. = 13, $\frac{N}{2}$ = 25

M = $l + \dfrac{i}{f} × \left ( \dfrac{N}{2} - c.f. \right ) $

$= 20 + \dfrac{10}{15} × (25-13)$

$= 20 + 8$

$= 28$

Now,

Arranging the data in a table:

Class	Frequency (f)	Mid Value(x)	|x-M|	f|x-M|
0-10	6	5	23	138
10-20	7	15	13	91
20-30	15	25	3	45
30-40	16	35	7	122
40-50	4	45	17	68
50-60	2	55	27	54
				$\sum$f|x-M| = 508

Now,

Mean Deviation about the median (M.D.) = $\dfrac{\sum f|x-M|}{N}$

$= \dfrac{508}{50}$

$= 10.16$

Hence, the required mean deviation about the median of the above data is 10.16.

Related Notes and Solutions:

Here is the website link to the notes of Statistics of Class 10.

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