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

${MD} =\frac{\sum{f|x-Me|}}{N} = \frac{\sum{f|D|}}{N}$

Where −

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

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

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

${Me} = \frac{215}{11} \\[7pt] \, = {19.54}$

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

${MD} = \frac{\sum{f|D|}}{N} \\[7pt] \, = \frac{103.62}{11} \\[7pt] \, = {9.42}$

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

${=\frac{MD}{Me}} \, = \frac{9.42}{19.54} \\[7pt] \, = {0.48}$

The Mean Deviation of the given numbers is 9.42.

The coefficient of mean deviation of the given numbers is 0.48.