5.46 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSMeasures of Central Tendency and Measures of Dispersion
Coefficient of Range :
The formulae of this relative measure is
difference of extreme value i.e. range
sum of extreme valesIn the above example, Coefficient of range =30 10 40 2^3 0 10 20+− = =^1 =0.5
Advantages of Range : Range is easy to understand and is simple to compute.
Disadvantages of Range :
It is very much affected by the extreme values. It does not depend on all the observations, but only on the
extreme values. Range cannot be computed in case of open-end distribution.
Uses of Range :
It is popularly used in the field of quality control. In stock-market fluctuations range is used.
5.3.2.2. Mean Deviation (or Average Deviation) :
Mean deviation and standard deviation, however, are computed by taking into account all the observations
of the series, unlike range.
Definition :
Mean deviation of a series is the arithmetic average of the deviations of the various items from the median
or mean of that series.
Median is preferred since the sum of the deviations from the median is less than from the mean. So the
values of mean deviation calculated from median is usually less than that calculated from mean.
Mode is not considered, as its value is indeterminate.
Mean deviation is known as First Moment of dispersion.
Computation of Mean Deviation :
(a) For individual Observation (or Simple Variates)The formula is Mean Deviation (M.D.)
|d|
= n
∑Where | d | within two vertical lines denotes deviations from mean (or median), ignoring algebraic signs
(i.e., + and –).
Coefficient of Mean Deviation:
Coefficient of Mean Deviation =
Mean Deviation about Mean (or Median) 100%
Mean (or Median) ×
Steps to find M. D.
(1) Find mean or median
(2) Take deviation ignoring ± signs
(3) Get total of deviations
(4) Divide the total by the number of items.
Example 45 : To find the mean deviation of the following data about mean and median :
(`) 2, 6, 11, 14, 16, 19, 23.