Lecture 6/Measures of Dispersion/2018-2019 /

MEASURES OF DISPERSION
We know that averages are representatives of a frequency distribution but they fail to give
a complete picture of the distribution. They do not tell anything about the scatterness of
observations within the distribution.

Suppose that we have the distribution of the yields (kg per plot) of two paddy varieties
from 5 plots each. The distribution may be as follows:
VarietyI 45 42 42 41 40
VarietyII 54 48 42 33 30
It can be seen that the mean yield for both varieties is 42 kg. But we can not say that the
performance of the two varieties is same. There is greater uniformity of yields in the first
variety whereas there is more variability in the yields of the second variety. The first
variety may be preferred since it is more consistent in yield performance. From the above
example, it is obvious that a measure of central tendency alone is not sufficient to
describe a frequency distribution. In addition to it we should have a measure of
scatterness of observations. The scatterness or variation of observations from their
average is called the dispersion. There are different measures of dispersion like the range,
the quartile deviation, the mean deviation and the standard deviation.



RANGE

The simplest measure of dispersion is the range. The range is the difference between the
minimum and maximum values in a group of observations for example, suppose that the
kapas yields (kg per plot) of a cotton variety from five plots are 8, 9, 8, 10 and 11. The
range is (11 - 8) = 3 kg. In practice the range is indicated as 8 - 11 kg.

Range takes only the maximum and minimum values into account and not all the values.
Hence it is a very unstable or unreliable indicator of the amount of deviation. It is affected
by extreme values. In the above example, if we have 15 instead of figure 11, the range
will be (8 - 15) = 7 kg.

In order to avoid these difficulties another measure of dispersion called quartile deviation
is preferred.