A frequency distribution is a statistical tool that describes the number of observations for each possible value of a variable. It is a way to organize and present frequency counts so that the information can be interpreted more easily. The frequency of a value is the number of times it occurs in a dataset, and a frequency distribution is the pattern of frequencies of a variable.

There are four types of frequency distributions: ungrouped frequency distributions, grouped frequency distributions, relative frequency distributions, and cumulative frequency distributions. Ungrouped frequency distributions show the number of observations of each value of a variable, and they are used when you’re more interested in comparing frequencies than the actual number of observations. Grouped frequency distributions show the sum of the frequencies less than or equal to each value or class interval of a variable, and they are used for ordinal or quantitative variables when you want to understand how often observations fall below certain values. Relative frequency distributions show the proportion of observations in each category, and they are used when you want to compare the frequencies of different categories. Cumulative frequency distributions show the number of observations that fall below a certain value or class interval, and they are used when you want to understand the proportion of observations that fall below certain values.

Frequency distributions are often displayed using frequency tables, which are an effective way to summarize or organize a dataset. A frequency table is usually composed of two columns: the values or class intervals and their frequencies. The method for making a frequency table differs between the four types of frequency distributions. Frequency distributions can also be displayed using graphs, such as histograms, bar graphs, frequency polygons, and so on.

In summary, a frequency distribution is a way to organize and present frequency counts so that the information can be interpreted more easily. It describes the number of observations for each possible value of a variable and can be displayed using frequency tables or graphs. There are four types of frequency distributions: ungrouped, grouped, relative, and cumulative.