Lecture 3n.docx - Lecture-8-9 Measures of Dispersion The...

Lecture-8-9
Measures of Dispersion
The measures of central tendency, such as the mean, median, and mode, do not reveal the
whole picture of the distribution of a data set. Two data sets with the same mean may
have completely different spreads. The variation among the values of observations for
one data set may be much larger or smaller than for the other data set. Consider the
following two data sets on the ages (in years) of all workers working for each of two
small companies.
Company 1: 47, 38, 35, 40, 36, 45, 39
Company 2: 70, 33, 18, 52, 27
The mean age of workers in both these companies is the same, 40 years. If we do not
know the ages of individual workers at these two companies and are told only that the
mean age of the workers at both companies is the same, we may deduce that the workers
at these two companies have a similar age distribution. As we can observe, however, the
variation in the workers’ ages for each of these two companies is very different.
Company 1 36 39
35 38 40 45 47
Company 2
18 27 33 52 70
Thus, the mean, median, or mode by itself is usually not a sufficient measure to reveal the
shape of the distribution of a data set. We also need a measure that can provide some
information about the variation among data values. The measures that help us learn about
the spread of a data set are called the measures of dispersion . The measures of central
tendency and dispersion taken together give a better picture of a data set than the
measures of central tendency alone.
Different Measures of Dispersion:
(i) Range
(ii) Variance
(iii) Standard deviation and
(iv) Coefficient of variation
1

Range
The range is the simplest measure of dispersion to calculate. It is obtained by taking the
difference between the largest and the smallest values in a data set.
Finding the Range for Ungrouped Data
Range = Largest value - Smallest value
EXAMPLE
Table 1 gives the total areas in square miles of the four western South-Central states of
the United States.