Statistics - Mean Deviation of Discrete Data Series

When data is given alongwith their frequencies. Following is an example of discrete series:

Items	5	10	20	30	40	50	60	70
Frequency	2	5	1	3	12	0	5	7

For discrete series, the Mean Deviation can be calculated using the following formula.

Formula

${MD} =\frac{\sum{f|x-Me|}}{N} = \frac{\sum{f|D|}}{N}$

Where −

The Coefficient of Mean Deviation can be calculated using the following formula.

${Coefficient\ of\ MD} =\frac{MD}{Me}$

Problem Statement:

Calculate Mean Deviation and Coefficient of Mean Deviation for the following discrete data:

Items	14	36	45	50	70
Frequency	2	5	1	1	3

Solution:

Based on the given data, we have:

${x_i}$	Frequency ${f_i}$	${f_ix_i}$	${\|x_i-Me\|}$	${f_i\|x_i-Me\|}$
14	2	28	31	62
36	5	180	9	45
45	1	45	0	0
50	1	50	5	5
70	3	210	15	45
	${N=12}$			${\sum {f_i\|x_i-Me\|} = 157}$

Median

${Me = (\frac{N+1}{2})^{th}\ Item \\[7pt] \, = (\frac{6}{2})^{th}\ Item \, = 3^{rd}\ Item \, = 45}$

Based on the above mentioned formula, Mean Deviation ${MD}$ will be:

${MD} = \frac{\sum{f|D|}}{N} \\[7pt] \, = \frac{157}{12} \\[7pt] \, = {13.08}$

and, Coefficient of Mean Deviation ${MD}$ will be:

${=\frac{MD}{Me}} \, = \frac{13.08}{45} \\[7pt] \, = {0.29}$

The Mean Deviation of the given numbers is 13.08.

The coefficient of mean deviation of the given numbers is 0.29.