Unimodal Distribution

This is a DISTRIBUTION of values for a single VARIABLE that only has one mode and a single “peak.” The mode is one of three common measures that are used to determine a variable's “typical score” and is the most frequently occurring value of any given variable (Lewis-Beck, 1995, p. 8).

An example of a unimodal distribution is the standard NORMAL DISTRIBUTION. This distribution has a MEAN of zero and a STANDARD DEVIATION of 1. In this particular case, the mean is equal to the MEDIAN and mode. Moreover, the standard normal distribution [Page 1157]only has a single, equal mean, median, and mode. Therefore, it is a unimodal distribution because it only has one mode.

Figure 1 Histogram for Household Income at Selected Percentiles

However, a unimodal distribution does not have to have SYMMETRY like the standard normal distribution. A unimodal distribution can also be SKEWED to the left or right. An example of such a distribution is that of income in the United States.

Figure 1 illustrates the annual income of the U.S. population by different categories (DeNavas-Walt & Cleveland, 2002, p. 20). The MEDIAN income, in which half of the values are greater and half are smaller, falls in the $42,228 category. This figure suggests that the distribution of American household income is somewhat skewed to the left because the median is closer to the bottom 10% (at $10,913) than to the top 10% of all households (at $150,499). Furthermore, the modal category is $42,228. There is a much larger percentage of households (about 50%) in this income category than in the other income categories, indicating the distribution is clearly unimodal.

Regardless of whether a unimodal distribution is skewed or symmetric, it must have a single “peak.” A distribution with a single “peak” is one in which there is a single most frequently occurring value of any given variable, as illustrated by its FREQUENCY DISTRIBUTION. If a distribution has two “peaks,” then it is a BIMODAL DISTRIBUTION. Finally, if a distribution has more than two “peaks,” then it is a MULTIMODAL DISTRIBUTION.