Frequency distribution//Class interval /limit/ boundary//cumulative frequency /relative frequency

A frequency distribution in statistics is a table or graph that shows how often values or groups of values occur within a dataset. It organizes raw data into a more understandable format, showing the frequency (count) for each possible outcome or interval, making it easier to spot patterns and trends. These distributions can be visualized in a table or a chart and are useful for summarizing large sets of data, according to Scribbr, Investopedia, Cuemath, and Verywell Mind.


Key features

Frequency:
The number of times a specific value or data point appears in a dataset.

Classes/Intervals:
Groups of values that are used to organize continuous data. For example, an interval could be "5'0"-5'2"".

Class Width:
The range of values within each class. It is ideally the same for all classes to ensure comparability.

Frequency Table:
A table that lists the classes or values alongside their frequencies.

Types of frequency distributions

Ungrouped Frequency Distribution:
Lists the frequency for each individual data value, without grouping them.

Grouped Frequency Distribution:
Groups data values into intervals, which is helpful for large datasets with continuous data.

Relative Frequency Distribution:
Shows the proportion (or percentage) of the total data that falls into each class, rather than the raw count.

Cumulative Frequency Distribution:
Shows the total number of observations that are less than or equal to a specific value or class interval.


Uses of frequency distributions


Summarizing data:
They provide a concise summary of a large dataset.

Visualizing patterns:
They make it easier to see the shape of the data, such as a normal distribution.

Calculations:
They are the basis for calculating other statistics, such as the mean, median, and mode.

Comparisons:
They can be used to compare different datasets. For example, a frequency polygon can be used to compare two frequency distributions.