Elementary Statistics and Computer Application

Measures of Dispersion

• The 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
Variety I	45	42	42	41	40
Variety II	54	48	42	33	30


• It can be seen that the mean yield for both varieties is 42 kg but cannot say that the performances of the two varieties are 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.Form 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 are called the dispersion. There are different measures of dispersion like the range, the quartile deviation, the mean deviation and the standard deviation.

Characteristics of a good measure of dispersion
An ideal measure of dispersion is expected to possess the following properties

1. It should be rigidly defined
2. It should be based on all the items.
3. It should not be unduly affected by extreme items.
4. It should lend itself for algebraic manipulation.
5. It should be simple to understand and easy to calculate