Frequency Distribution

Frequency distribution is a statistical method used to organize and summarize data in a clear and meaningful way. It shows how often each individual value or range of values occurs within a dataset. By arranging the data into categories or intervals and counting the number of observations in each category, frequency distribution helps in identifying patterns, trends, and the overall distribution of data. This method is especially useful when dealing with large amounts of raw data, as it simplifies complex information and supports further analysis through graphs and charts.

Definition of Frequency Distribution

Frequency distribution is a systematic arrangement of data that shows the number of times each value or group of values occurs in a dataset. It helps in organizing raw data into a clear format for easy interpretation and analysis.

Types of Frequency Distribution

Frequency distribution can be broadly categorized into the following types based on how the data is organized and presented:

1. Ungrouped Frequency Distribution

An ungrouped frequency distribution is used when the dataset is small and contains only a limited number of distinct values. In this type, each unique data value is listed individually along with its corresponding frequency — the number of times that value occurs in the dataset.

This format is straightforward and best suited for discrete data, such as test scores, number of siblings, or shoe sizes. It allows a clear view of how frequently each particular value appears.

Example:

If the test scores of six students are: 3, 4, 3, 2, 4, 3
Then the ungrouped frequency table will be:

Score	Frequency
2	1
3	3
4	2

2. Grouped Frequency Distribution

When a dataset is large and contains a wide range of continuous values, it is more practical to organize it into intervals or classes. This type of frequency distribution is known as grouped frequency distribution. Instead of listing each value separately, values are grouped into class intervals (e.g., 0–10, 11–20), and the frequency of values falling within each interval is recorded.

This approach simplifies complex data and helps identify patterns and trends more easily. It is commonly used in surveys, population studies, and educational assessments.

Example:

Marks Range	Frequency
0 – 10	4
11 – 20	6
21 – 30	10

Here, instead of individual scores, the scores are grouped in ranges.

3. Cumulative Frequency Distribution

Cumulative frequency distribution shows the running total of frequencies up to a certain point in the dataset. It helps to determine how many values fall below or above a certain limit. There are two types of cumulative frequency distributions:

• Less than cumulative frequency: Shows the number of observations less than or equal to a particular class limit.
• More than cumulative frequency: Shows the number of observations greater than or equal to a particular class limit.

This type is particularly useful when calculating medians, quartiles, and percentiles.

Example (Less than type):

Marks (Less than)	Cumulative Frequency
< 10	4
< 20	10
< 30	18

Each cumulative frequency is the sum of all previous frequencies up to that class.

4. Relative Frequency Distribution

Relative frequency distribution presents the frequency of each class as a proportion or percentage of the total number of observations. It helps in understanding the proportion of data that falls within each category, which is particularly useful when comparing datasets of different sizes.

The relative frequency is calculated using the formula:
Relative Frequency = (Class Frequency / Total Frequency) × 100

Example:

Class Interval	Frequency	Relative Frequency (%)
0 – 10	5	25%
11 – 20	10	50%
21 – 30	5	25%

This distribution makes it easier to analyze percentages rather than absolute numbers.

Frequency Distribution Graphs

A frequency distribution graph is a visual representation of how data values are distributed across categories or intervals. It is created from a frequency table and helps in understanding the overall pattern, shape, and spread of data.

These graphs are commonly used in statistics, education, research, and data analysis to simplify complex datasets and make them easier to interpret.

Types of Frequency Distribution Graphs

1. Histogram

A histogram is used to represent continuous grouped data. It displays class intervals on the X-axis and frequencies on the Y-axis. The bars are adjacent (without gaps) to indicate continuity.

Use: Ideal for numerical data like height, weight, or test scores.

2. Bar Graph

A bar graph is used for discrete or ungrouped data. Each bar represents a specific category or value, and the height shows its frequency. Unlike histograms, bars do not touch.

Use: Suitable for categorical or ungrouped numerical data (e.g., number of students by grade).

3. Frequency Polygon

This is a line graph that connects points plotted using the midpoints of class intervals and their frequencies. It helps to understand the shape of the distribution.

Use: Best for comparing multiple distributions.

4. Pie Chart

A pie chart shows the relative frequency of different categories as sectors of a circle. Each sector represents a proportion of the total.

Use: Useful when showing percentage or part of a whole.

5. Cumulative Frequency Graph (Ogive)

This graph shows cumulative frequencies and is used to determine medians, percentiles, or how many observations fall below or above a certain value.

Use: Helpful in identifying trends over time or threshold levels.