Statistics - Mean Deviation of Continuous Data Series
When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
Items | 0-5 | 5-10 | 10-20 | 20-30 | 30-40 |
---|---|---|---|---|---|
Frequency | 2 | 5 | 1 | 3 | 12 |
In case of continous series, a mid point is computed as $\frac{lower-limit + upper-limit}{2}$ and Mean Deviation is computed using following formula.
Formula
Where −
${N}$ = Number of observations.
${f}$ = Different values of frequency f.
${x}$ = Different values of mid points for ranges.
${Me}$ = Median.
The Coefficient of Mean Deviation can be calculated using the following formula.
Example
Problem Statement:
Let's calculate Mean Deviation and Coefficient of Mean Deviation for the following continous data:
Items | 0-10 | 10-20 | 20-30 | 30-40 |
---|---|---|---|---|
Frequency | 2 | 5 | 1 | 3 |
Solution:
Based on the given data, we have:
Items | Mid-pt ${x_i}$ | Frequency ${f_i}$ | ${f_ix_i}$ | ${|x_i-Me|}$ | ${f_i|x_i-Me|}$ |
---|---|---|---|---|---|
0-10 | 5 | 2 | 10 | 14.54 | 29.08 |
10-20 | 15 | 5 | 75 | 4.54 | 22.7 |
20-30 | 25 | 1 | 25 | 6.54 | 5.46 |
30-40 | 35 | 3 | 105 | 14.54 | 46.38 |
${N=11}$ | ${\sum f=215}$ | ${\sum {f_i|x_i-Me|} = 103.62}$ |
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 9.42.
The coefficient of mean deviation of the given numbers is 0.48.