# Statistics - Mean Deviation of Individual Data Series

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

 Items 5 10 20 30 40 50 60 70

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:

 Items 14 36 45 70 105

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.