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
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.
Example
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
Based on the above mentioned formula, Mean Deviation ${MD}$ will be:
and, Coefficient of Mean Deviation ${MD}$ will be:
The Mean Deviation of the given numbers is 13.08.
The coefficient of mean deviation of the given numbers is 0.29.