Types of Frequency Distribution

A symmetric frequency distribution is a distribution in which the data are evenly distributed around the mean and the bars on each side of the middle bar are approximately the same height.

The mean and median are approximately equal in a symmetric frequency distribution. Therefore, the measures of center and spread that best describe a symmetric distribution are the mean and the standard deviation, respectively.

A skewed frequency distribution is a distribution in which the data is not spread evenly — rather, the data is clustered at one end. In this case, the mean and the median are not equal, causing the data set to be skewed. A skewed distribution is neither symmetric nor normal. In general, there are two types of skewed frequency distributions.

Skewed Distribution	Description
Skewed Left / Negatively Skewed	The distribution has a long left tail and the median is greater than the mean.
Skewed Right / Positively Skewed	The distribution has a long right tail and the median is less than the mean.

The difference between normal and skewed distributions can be visualized in the following applet. The measures of center and spread that best describe a skewed distribution are the median and the five-number summary, respectively. The median is preferred because it is less affected by outliers, while the mean will fall in the direction of the tail of the distribution.

A uniform frequency distribution, sometimes called a flat distribution, is a type of distribution where all the bars are about the same height. This type of distribution arises in scenarios where all the possible outcomes are equally likely. A uniform distribution is also symmetric.

As an example, the possible outcomes of rolling a fair six-sided die are $1,$ $2,$ $3,$ $4,$ $5,$ and $6,$ and they each have an equal probability of occurring. The following applet simulates rolling a die $100$ times and records the frequency of each outcome. It should be noted that even though each outcome is theoretically equally likely, the frequencies of the outcomes can actually be unequal when collecting data from a real experiment.

A bimodal distribution is a data distribution with a range of values near two individual values or two intervals, separating the data into two clusters. This causes the histogram of the data to have two peaks. The mean and the median of a bimodal distribution are near the center of the distribution.

The given distribution indicates that the sampling was likely made from two different populations. The term bimodal refers to the peaks of the distribution, which differs from the mode when intervals are used to make the data display. It is worth mentioning that a bimodal distribution whose bars are about the same height on each side of the peaks is also symmetric.

Example

Consider a histogram that shows the attendance per hour at a local restaurant.

The peaks represent typical lunch and dinner hours. Since the histogram has two distinct peaks, it has a bimodal distribution. Traffic patterns, heights, and test scores are other examples that can show bimodal distribution. Although histograms are mainly used to show bimodality, other representations such as dot plots and leaf plots can also show bimodality.