Measure of Central Tendency provides typical value about the data set, but it does not tell the actual story about the data i.e. mean, median, and mode are enough to get summary information, though we know about the center of the data. In other words, we can measure the center of the data by looking at averages (mean, median, and mode). These measures tell nothing about the spread of data. So for more information about data, we need some other measure, such as the Range measure of dispersion or spread.
Range Measure of Dispersion
The Spread of data can be measured by calculating the range of data; the range tells us how many numbers of data extend. The range is an absolute measure of dispersion that can be found by subtracting the highest value (called upper bound) in data from the smallest value (called lower bound). i.e.
Range = Upper Bound – Lowest Bound
OR
Range = Largest Value – Smallest Value
This absolute measure of dispersion has disadvantages as range only describes the width of the data set (i.e. only spread out) measured in the same unit as data, but it does not give the real picture of how data is distributed. If data has outliers, using range to describe the spread of that can be very misleading as the range is sensitive to outliers.
We need to be careful in using the range measure of dispersion as it does not give the full picture of what’s going between the highest and lowest values. It might give a misleading picture of the spread of the data because it is based only on the two extreme values. Therefore, Range is an unsatisfactory measure of dispersion.
However, the range measure of dispersion is widely used in statistical process control such as control charts of manufactured products, daily temperature, stock prices, etc., applications as it is very easy to calculate. It is an absolute measure of dispersion, its relative measure known as the coefficient of dispersion defines the relation
\[Coefficient\,\, of\,\, Dispersion = \frac{x_m-x_0}{x_m-x_0}\]
The coefficient of dispersion is pure dimensionless and is used for comparison purposes.