A statistician had one foot in a bucket of ice water and one foot in a bucket of boiling water. He said, "My feet feel great, on the average." He meant that the average temperature of the water in the two buckets was comfortable. This may be true, but the average temperature doesn't tell the entire story. What other measures of the temperature data would be useful in describing the statistician's situation, and why is it useful?

Answer:

In statistics, center (or central tendency or average) refers to a set of numerical summaries that attempt to describe what a typical data value might look like. These are “average” value or representative value of the data distribution. The more common notions of center or average are mean and median. The absurdity in this story points to the inadequacy of using center alone in describing a data distribution. To get a more complete picture, we need to use spread too.
Spread (or dispersion) refers to a set of numerical summaries that describe the degree to which the data are spread out. Some of the common notions of spread are range, 5-number summary, interquartile range (IQR), and standard deviation. A large spread indicates that there is a great deal of dispersion or scatter in the data. Thus, using spread, we can actually observe how much the data varies.
From here, we observe that, trusting on the central value alone might lead us to a wrong conclusion. It is always wise to consider the variation in the data as also the central value.