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Frequency Distribution

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.

FAQs

  1. What do you mean by frequency distribution?

    Frequency distribution is a statistical method that shows how often each value in a data set occurs. It organizes data into categories and displays the frequency (count) of observations in each category.

  2. What is the meaning of frequency distribution in PDF?

    In a statistical context, a frequency distribution in PDF (Probability Density Function) refers to a function that describes the likelihood of different outcomes in a continuous random variable, not just in tabular form but also mathematically.

  3. What is frequency in statistics?

    Frequency in statistics refers to how often a particular data point or range of data points appears in a given data set.

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