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Frequency Distribution

A frequency distribution, sometimes called a histogram distribution, is a representation that displays the number of observations within a given interval. It is used to show the empirical or theoretical frequency of occurrence of each possible value in a data set, often recorded in a frequency table. Frequency distributions of categorical data are typically presented using a bar graph.

In the case of numerical data, the graphical representation of a frequency distribution is called a histogram.

Depending on how a data set is distributed, its histogram can have different shapes. The most common types of distributions are symmetric frequency distribution and skewed frequency distribution.

Symmetric Frequency Distribution

In a symmetric frequency distribution, data are distributed evenly around the mean and the bars on each side of the middle bar are about the same height.

Additionally, the mean and median are approximately equal to each other in this type of frequency distribution.

Skewed Frequency Distribution

Not all data sets have a symmetric frequency distribution. If the mean and median are not equal, then the data set is skewed. 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 these three basic types of frequency distributions can be visualized in the following applet.
normal and skewed distribution

Distributions and Measures of Center and Variation

The measures of center and variation that best describe a given data set can be known in advance by looking at the shape of its distribution.

  • Symmetric Distribution: In this type of distribution, the mean and the standard deviation will best describe the center and variation of the data, respectively.
  • Skew Distribution: In this case, use the median to describe the center and the five-number summary to describe the spread of the data.

This comes from the fact that the mean and the median are about the same in a symmetric distribution. Moreover, in a skew distribution, 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.