What Is a Frequency Distribution?

A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval. The frequency is how often a value occurs in an interval while the distribution is the pattern of frequency of the variable.

The interval size depends on the data being analyzed and the goals of the analyst. The intervals must be mutually exclusive and exhaustive. Frequency distributions are typically used within a statistical context. Generally, frequency distributions can be associated with the charting of a normal distribution.

Understanding a Frequency Distribution

As a statistical tool, a frequency distribution provides a visual representation of the distribution of observations within a particular test. Analysts often use a frequency distribution to visualize or illustrate the data collected in a sample. For example, the height of children can be split into several different categories or ranges.

In measuring the height of 50 children, some are tall and some are short, but there is a high probability of a higher frequency or concentration in the middle range. The most important factors for gathering data are that the intervals used must not overlap and must contain all of the possible observations.

Visual Representation of a Frequency Distribution

Both histograms and bar charts provide a visual display using columns, with the y-axis representing the frequency count, and the x-axis representing the variable to be measured. In the height of children, for example, the y-axis is the number of children, and the x-axis is the height. The columns represent the number of children observed with heights measured in each interval.

In general, a histogram chart will typically show a normal distribution, which means that the majority of occurrences will fall in the middle columns. Frequency distributions can be a key aspect of charting normal distributions which show observation probabilities divided among standard deviations.

Frequency distributions can be presented as a frequency table, a histogram, or a bar chart. Below is an example of a frequency distribution as a table.

Height of Children in a School
Interval (Height)	4'	4'5"	5'	5'2"
Frequency	2	5	6	3

Frequency Distribution in Trading

Frequency distributions are not commonly used in the world of investments; however, traders who follow Richard D. Wyckoff, a pioneering early 20th-century trader, use an approach to trading that involves frequency distribution.

Investment houses still use the approach, which requires considerable practice, to teach traders. The frequency chart is referred to as a point-and-figure chart and was created out of a need for floor traders to take note of price action and to identify trends.

The y-axis is the variable measured, and the x-axis is the frequency count. Each change in price action is denoted in Xs and Os. Traders interpret it as an uptrend when three X's emerge; in this case, demand has overcome supply. In the reverse situation, when the chart shows three O's, it indicates that supply has overcome demand.

The Bottom Line

A frequency distribution is used to display the number of observations within a particular interval. This method, while not always commonly used in investing, is still used by some traders. In this case, the frequency chart is called a point-and-figure chart and is used to identify trends through the observation of price action.