Question

M.D from Median in continuous series

Answer 1

Answer:

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 lower−limit+upper−limit2 and Mean Deviation is computed using following formula.

Formula

MD=∑f|x−Me|N=∑f|D|N

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.

Coefficient of MD=MDMe

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

xi Frequency

fi fixi |xi−Me| fi|xi−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 ∑f=215   ∑fi|xi−Me|=103.62

Median

Me=21511=19.54

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

MD=∑f|D|N=103.6211=9.42

and, Coefficient of Mean Deviation MD will be:

=MDMe=9.4219.54=0.48

The Mean Deviation of the given numbers is 9.42.

The coefficient of mean deviation of the given numbers is 0.48

Explanation: