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Unit 7: Measures of Dispersion
Demerits Notes
1. It is not based on all the observations.
2. It is very much affected by extreme observations.
3. It only gives rough idea of spread of observations.
4. It does not give any idea about the pattern of the distribution. There can be two distribution
with the same range but different patterns of distribution.
5. It is very much affected by fluctuations of sampling.
6. It is not capable of being treated mathematically.
7. It cannot be calculated for a distribution with open ends.
7.5.2 Uses of Range
Inspite of many serious demerits, it is useful in the following situations:
1. It is used in the preparation of control charts for controlling the quality of manufactured
items.
2. It is also used in the study of fluctuations of, say, price of a commodity, temperature of a
patient, amount of rainfall in a given period, etc.
Self Assessment
Fill in the blanks:
19. The ................................... of a distribution is the difference between its two extreme
observations.
20. Symbolically, R = L – S where R denotes range, L and S denote ...............................
observations, respectively.
21. A relative measure of range, also termed as the .............................
7.6 Interquartile Range
Interquartile Range is an absolute measure of dispersion given by the difference between third
quartile (Q ) and first quartile (Q )
3 1
Symbolically, Interquartile range = Q – Q .
3 1
7.6.1 Interpercentile Range
The difficulty of extreme observations can also be tackled by the use of interpercentile range or
simply percentile range.
Symbolically, percentile range = P – P (i < 50).
(100 - i) i
This measure excludes i% of the observations at each end of the distribution and is a range of the
middle (100 – 2i)% of the observations.
Normally, a percentile range corresponding to i = 10, i.e., P – P is used. Since Q = P and
90 10 1 25
Q = P , therefore, interquartile range is also a percentile range.
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