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, X | Deviation, |D| |
|---|---|
| 14 | 40 |
| 36 | 18 |
| 45 | 9 |
| 70 | 16 |
| 105 | 51 |
| ${\sum{|D|}}$ = 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.
Advertisements