Statistics - Mean Deviation of Individual Data Series

When data is given on individual basis. Following is an example of individual series:

Items510203040506070

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

Formula

${MD} =\frac{1}{N} \sum{|X-A|} = \frac{\sum{|D|}}{N}$

Where −

  • ${MD}$ = Mean deviation.

  • ${X}$ = Variable values

  • ${A}$ = Average of choices

  • ${N}$ = Number of observations

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

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

Example

Problem Statement:

Calculate Mean Deviation and coefficient of mean deviation for the following individual data:

Items14364570105

Solution:

${A} = \frac{14+36+45+70+105}{5} = \frac{270}{5} = 54$
Item, XDeviation, |D|
1440
3618
459
7016
10551
 ${\sum{|D|}}$ = 134

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

${MD} =\frac{1}{N} \sum{|X-A|} = \frac{\sum{|D|}}{N} \, = \frac{134}{5} \\[7pt] \, = {26.8}$

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

${=\frac{MD}{A}} \, = \frac{26.8}{54} \\[7pt] \, = {0.49}$

The Mean Deviation of the given numbers is 26.8.

The coefficient of mean deviation of the given numbers is 0.49.

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