Measures of Central Location

Perhaps you have heard a statement like "The average number of automobiles owned by households in the United States is 1.37," and have been amused at the thought of a fraction of an automobile sitting in a driveway. In such a context the following measure for central location might make more sense.

Definition

The population mode is defined in a similar way, but we will not have occasion to refer to it again in this text.

On a relative frequency histogram, the highest point of the histogram corresponds to the mode of the data set. Figure 2.9 "Mode" illustrates the mode.

Figure 2.9 Mode

EXAMPLE 8

$\begin{array}{llll}-1 & 0 & 2 & 0\end{array}$

Solution:

The value $\mathrm{0}$ is most frequently observed and therefore the mode is $\mathrm{0}$.

EXAMPLE 9

Solution:

The two most frequently observed values in the data set are $\mathrm{1}$ and $\mathrm{2}$. Therefore mode is a set of two values: $\{1,2\}$.

The mode is a measure of central location since most real-life data sets have more observations near the center of the data range and fewer observations on the lower and upper ends. The value with the highest frequency is often in the middle of the data range.