Statistics - Mean Deviation of Discrete Data Series


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

Items510203040506070
Frequency251312057

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 −

  • ${N}$ = Number of observations.

  • ${f}$ = Different values of frequency f.

  • ${x}$ = Different values of items.

  • ${Me}$ = Median.

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

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

Example

Problem Statement:

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

Items1436455070
Frequency25113

Solution:

Based on the given data, we have:

${x_i}$Frequency
${f_i}$
${f_ix_i}$${|x_i-Me|}$${f_i|x_i-Me|}$
142283162
365180945
4514500
5015055
7032101545
 ${N=12}$  ${\sum {f_i|x_i-Me|} = 157}$

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.

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