Definition:

A frequency distribution is a tabular summary of grouped data that describes the frequency of occurrence of different values or classes. It provides a breakdown of the data into intervals, or classes, and the number of observations that fall into each interval.

Components of a Frequency Distribution:

• Class Intervals: The intervals used to group the data.
• Class Boundaries: The limits of each class interval.
• Class Frequencies: The number of observations that fall into each interval.
• Relative Frequencies: The frequencies divided by the total number of observations, expressed as a proportion.
• Cumulative Frequencies: The sum of the frequencies of all intervals up to a given interval.

Types of Frequency Distributions:

• Discrete: Data that can be counted or grouped into discrete intervals.
• Continuous: Data that can be measured continuously, such as height or weight.

Uses of Frequency Distributions:

• Describing the distribution of data.
• Analyzing trends and patterns.
• Comparing groups or samples.
• Constructing histograms and ogives.
• Calculating measures of central tendency and dispersion.

Example:

| Class Interval | Frequency ||—|—|| 0-10 | 20 || 10-20 | 30 || 20-30 | 40 || 30-40 | 20 |

This frequency distribution describes a set of data with three classes: 0-10, 10-20, and 20-30. The frequency of each class is shown in the table, with a total frequency of 110.

Key Points:

• Frequency distribution summarizes grouped data by describing the frequency of occurrence of different values or classes.
• Components of a frequency distribution include class intervals, class boundaries, class frequencies, relative frequencies, and cumulative frequencies.
• Types of frequency distributions include discrete and continuous.
• Frequency distributions are used for various purposes, such as describing data distribution, analyzing trends, and comparing groups.