Last updated on July 4th, 2025
A frequency distribution table is a chart that presents the frequency of each category or data in an organized way. It represents how often each value occurs and helps identify patterns within a dataset. When collecting data, we need to organize the data into a frequency distribution table. This table summarizes the data by grouping it into different categories or variables, and their frequencies. In this topic, we will learn the essentials of the frequency distribution table and its properties.
In a dataset, how often something occurs is expressed by its frequency. In statistics, frequency distribution is a tool that is used for data organization and to make meaningful decisions. How often a value appears in a dataset can be understood by a frequency distribution. It shows where the most values are concentrated and where the least values are presented. Tabularly or graphically, we can represent the frequency distribution.
To visually represent a frequency distribution table, we use a frequency distribution graph. Graphical elements, such as bars, lines, and curves are used to express how frequently various values occur. These graphs help us to simplify complex data, figure out new trends, and make informed decisions. The various methods for representing the frequency distribution are:
A histogram is used for representing numerical data, and it is similar to a bar graph. The y-axis of the histogram indicates frequencies, and the x-axis represents interval classes. Remember, there is no gap between the bars of a histogram. For example, here is a frequency table explaining the number of survey respondents in each age group.
Age (years) | Frequency |
10 - 20 | 10 |
20 - 30 | 15 |
30 - 40 | 5 |
40 - 50 | 5 |
50 - 60 | 3 |
The histogram showing the ages of survey respondents is:
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Bar graphs use rectangular bars to represent the data on the x-axis and y-axis. The height and length of the bars show the frequency of categories or values. The bar graph is commonly used to express the frequency of ungrouped data in a flexible sequence. Remember to always leave gaps between the bars to separate the categories clearly. For e.g., the distribution table representing a dataset of kids and their favorite ice cream flavors will look like this:
Ice cream flavor | Number of kids (frequency) |
Vanilla | 6 |
Chocolate | 7 |
Strawberry | 3 |
Mango | 4 |
Butterscotch | 8 |
The following is a bar graph representing the frequency of kids and their favorite ice cream flavors.
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In a frequency polygon, the data is visually represented by plotting dots at the midpoints of each class interval and joining them with straight lines to form a polygon. For example, here is a dataset that shows the number of young people enjoying different genres of movies.
Movies | Number of Young People (frequency) |
Action | 72 |
Science fiction | 55 |
Comedy | 40 |
Horror | 42 |
Romance | 38 |
Here is the frequency polygon, representing the frequency of youth and their favorite movie genres.
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The pie chart represents data in a circular format. Each category is represented as a slice of an entire circle, and the size of each slice shows its proportion of the total dataset. For example, the frequency distribution table of kids who prefer different fruits is given below:
Fruit | Number of kids (frequency) |
Apple | 8 |
Orange | 5 |
Pineapple | 7 |
Strawberry | 4 |
Mango | 6 |
Here, the pie chart of the given frequency distribution table is given below.
Here, when we convert a number into a percentage, use the formula:
Percentage = Frequency of a category / Total frequency × 100
So, total frequency = 8 + 5 + 7 + 4 + 6 = 30
Frequency of Apple = 8 / 30 × 100 = 26. 7%
Frequency of Orange = 5/ 30 × 100 = 16.7%
Frequency of Pineapple = 7/ 30 × 100 = 23.3%
Frequency of Strawberry = 4 / 30 × 100 = 13.3%
Frequency of Mango = 6 / 30 × 100 = 20
Depending on the nature of the collected data, frequency distribution is classified into different types. The collected data is organized in a meaningful way to clearly understand the nature, pattern, and trends and to make better decisions. The four types of frequency distribution are:
The observations or data in a grouped frequency distribution are divided into different intervals. Then, the frequencies of each class interval are counted. When we have a very large set of data, this type of frequency distribution is useful to make data much easier to understand.
For example, the data given in a grouped frequency distribution is categorized into different groups of equal sizes. Then, the number of times each class interval or category appears is marked against each interval. The frequency distribution table for grouped data is given below:
Weight of students | Number of students (frequency |
25 - 30 | 3 |
31 - 35 | 6 |
36 - 40 | 5 |
41 - 45 | 2 |
In an ungrouped frequency distribution, the distinct observations or data are collected and counted separately. When we have a small dataset, the ungrouped frequency distribution is useful. For instance, if we have to count the marks of 15 students in a class, we can apply this type of frequency distribution. The frequency distribution table of an ungrouped dataset is:
Marks scored | Number of students (frequency) |
5 | 1 |
11 | 3 |
16 | 1 |
22 | 2 |
27 | 4 |
35 | 2 |
40 | 2 |
The percentage or proportion of observations in each class is represented by relative frequency distribution. We use this type of distribution to compare several data sets or to understand the distribution of data within a single set by expressing frequencies as percentages. The formula for relative frequency is:
Relative frequency = Frequency of event / total number of events
For example, the relative frequency distribution table for the following data is:
Marks scored | Number of kids (frequency) |
0 - 10 | 8 |
11 - 20 | 5 |
21 - 30 | 7 |
31 - 40 | 4 |
41 - 50 | 6 |
The relative frequency distribution table:
Marks scored | Number of kids (frequency) | Relative frequency |
0 - 10 | 8 | 8 / 30 = 0.26 |
11 - 20 | 5 | 5 / 30 = 0.16 |
21 - 30 | 7 | 7 / 30 = 0.23 |
31 - 40 | 4 | 4 / 30 = 0.13 |
41 - 50 | 6 | 6 / 30 = 0.20 |
Cumulative frequency is the running total of all frequencies up to a specific value or interval. The two types of cumulative frequency distributions are:
45 | 34 | 75 |
26 | 9 | 50 |
97 | 8 | 15 |
57 | 88 | 86 |
33 | 47 | 63 |
64 | 70 | 74 |
Here, we have a lot of distinct values. So, we will categorize these values in a grouped distribution frequency table.
Marks | Frequency |
0 - 10 | 2 |
10 - 20 | 1 |
20 - 30 | 1 |
30 - 40 | 2 |
40 - 50 | 3 |
50 - 60 | 1 |
60 - 70 | 3 |
70 - 80 | 2 |
80 - 90 | 2 |
90 - 100 | 1 |
Next, we can convert this frequency distribution table into a cumulative frequency distribution table.
Marks scored by Miya | Cumulative frequency |
Less than 10 | 2 |
Less than 20 | 2 + 1 = 3 |
Less than 30 | 4 |
Less than 40 | 6 |
Less than 50 | 9 |
Less than 60 | 10 |
Less than 70 | 13 |
Less than 80 | 15 |
Less than 90 | 17 |
Less than 100 | 18 |
Next, the cumulative frequency distribution of the second type which is more than cumulative frequency.
Marks scored by Miya | Cumulative frequency |
More than 10 | 18 |
More than 20 | 18 - 2 = 16 |
More than 30 | 15 |
More than 40 | 14 |
More than 50 | 12 |
More than 60 | 9 |
More than 70 | 8 |
More than 80 | 5 |
More than 90 | 3 |
More than 100 | 1 |
While making a frequency distribution table, we have to adhere to several steps. They are as follows:
Step 1: Design a table with two columns. One for frequency and the other for the data we need to organize.
Step 2: Decide whether we need a grouped frequency distribution table or an ungrouped frequency distribution table by analyzing the items in the given dataset. When we have a very large set of data, then better we go with a grouped frequency distribution table.
Step 3: In the first column, categorize the data set values.
Step 4: Identify the frequency of each category by counting them and allocate it to the second column.
Step 5: Finally, write the total frequency in the last row of the frequency distribution table.
By following these steps, we can create an organized and well-structured frequency distribution table for the given dataset.
Frequency distribution is a tool used in statistics to organize data and make insightful conclusions. A frequency distribution table is a chart that presents the frequency of each category or data in an organized way. It represents how often each value occurs in a given dataset. The real-life applications of the frequency distribution table are countless. They are given below.
Frequency distribution tables are crucial for comparing multiple sets of data easily. It represents the data in a structured manner, and it allows us to understand the different trends and patterns from the dataset. However, some common mistakes can lead us to incorrect calculations and conclusions. Here are some of the common errors and their solutions that will help to obtain better results.
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!