Frequency Distribution Table in Statistics with Examples

Frequency Distribution Table: The Frequency Distribution Table in statistics provides the information on the number of occurrences (frequency) of different values distributed within a given time or over a given interval in a list, table or graphical representation. The frequency distribution table refers to the data in the tabular form with two columns corresponding to the particular data and its frequency.

With the help of a frequency distribution table, researchers can analyse the entire data easily and conveniently. They can see any trend emerging from the data. A frequency distribution shows if the observations or data are concentrated in one area or if they are consistent or not. This is important when we have to process large amounts of data. This article will provide everything about frequency distribution and why it is important. We will also see how to make a frequency distribution table with examples. Read on to find out more!

What is Frequency?

The frequency of any value of the data is the number of times that value occurs in the given data set. In general, frequency is something how often it occurs in the data.

For example, if we ask the favourite colours of five people, they said their favourite colours are blue, red, white, black, and red.

Here, two students said their favourite colour is red. So, the frequency of red colour is two.

Thus, the frequency of the data tells the number of times that value appears in the given data.

Frequency Distribution of Table Definition

In our daily life, we will get a lot of information in the form of charts, figures and graphs, etc. There can be varied information, such as marks secured by the students, population of different countries, temperatures of various cities, etc.

Thus, the information that is collected is called the data. Well, once the data is collected, it should be represented in a meaningful way to be understood easily. A frequency distribution table is one of the ways to organise the data. It summarises the complete collected data in the form of a table.

In statistics, the frequency distribution table refers to the data in the tabular form with two columns corresponding to the particular data and its frequency.

Frequency Distribution Table Example:

An \({\rm{N}}{\rm{.G}}{\rm{.O}}\) conducted a blood donation camp for \(30\) people, whose blood groups are recorded as follows:

The above data can be represented in the form of a frequency distribution table as follows:

From the above table, we can observe that all the data is arranged in two columns, which can easily be understood.

Learn Cumulative Frequency Distribution

Types of Frequency Distribution Table

The frequency distribution table gives the information of the collected data in well designed tabular form to analyse the data quickly. There are different types of frequency distribution tables according to the representation of data. They are

1. Ungrouped frequency distribution table
2. Grouped frequency distribution table
3. Cumulative frequency distribution table
4. Relative frequency distribution table
5. Relative cumulative frequency distribution table

In this article, our scope of discussion will be limited to an ungrouped and grouped frequency distribution table only.

The general types of frequency distribution tables are grouped and ungrouped frequency distribution tables.

Ungrouped Frequency Distribution Table

An ungrouped frequency distribution table is the representation of each data separately with its frequency. This type of table is used for the smaller set of data. Ungrouped data is the data given in individual points.

Example:

The marks, scored by \(20\) students in a test are given below:

The tabular form of the above data can be given as follows:

The above tabular form of representing the data is known as the ungrouped frequency table, as it describes the frequency of individual data.

Grouped Frequency Distribution Table

Let us consider marks secured by \(100\) students at the school. It is tough to construct the frequency distribution table for each data, i.e., each student’s scores at the school. In this case, the table becomes lengthy and very difficult.

To overcome this problem, we will make the data into some groups known as class intervals.

Example:

The marks secured by \(100\) students are given as follows:

The frequency table for the above data can be drawn as follows by using the class intervals

How to Construct Frequency Distribution Table?

The frequency distribution table is constructed by using the tally marks. Tally marks are a form of a numerical system with the vertical lines used for counting. The cross line is placed over the four lines to get a total \(5\).

Example:
Consider a jar containing the different colours of pieces of bread as shown below:

Construct a frequency distribution table for the data mentioned above.

Answer:

Applications of Frequency Distribution Table

The two types of frequency distribution tables are the ungrouped frequency distribution table and grouped frequency distribution table. Some of the observations made from this method are as follows:

1. The table used to measure the frequency of the data
   From the table, we can observe the number of times the data appears in the data using frequency.
2. The table helps measures the dispersion, i.e. range, variance, and standard deviation.
   The range is the difference between higher and lower values of the given data.
3. Measures of central tendency and location, i.e. mean, median, and mode.
4. The table helps to determine the extent of the symmetry or asymmetry.

Let us understand the concept through some frequency distribution table examples.

Frequency Distribution Calculator

The frequency distribution calculator constructs a frequency distribution table, providing a snapshot view of the characteristics of a dataset. The calculator spits out some other data descriptors, such as mean, median, and skewness.

Solved Examples

Q.1. There are \(5\) students in a classroom. The teacher asked the students to talk about their favourite subjects. The results are listed below:

By looking at the above data, which is the most liked subject?
Ans:

Representing the above data in the frequency distribution table by using tally marks as follows

From the above table, we can see that the maximum number of students \(7\) likes mathematics.

Q.2. Construct the frequency distribution table for the data on heights in \({\rm{cm}}\) of \(20\) boys using the class intervals \(130\, – 135,135 – 140\) and so on. The heights of the boys in cm are:

Ans: The frequency distribution for the above data can be constructed as follows:

Q.3. Runs scored by Rohit Sharma in \(10\) International matches are recorded as follows:

Construct an ungrouped frequency distribution table for the given data.
Ans:

Q.4. The frequency distribution of the weights (in \({\rm{kg}}\)) \(40\) persons are given below:

Which class interval has the highest frequency and which has the lowest frequency?

Ans:

The frequency distribution of the weights \({\rm{kg}}\)) \(40\) persons is given below:

From the above data, the frequency of the class interval \({\rm{40}}\,{\rm{ – }}\,{\rm{45}}\) is \(14\) which is the maximum among all the frequencies.
And, the class interval \({\rm{50}}\,{\rm{ – }}\,{\rm{55}}\) is \(3\) which is the minimum among all the frequencies.
Therefore, the class interval \({\rm{40}}\,{\rm{ – }}\,{\rm{45}}\) has the highest frequency, and the interval \({\rm{50}}\,{\rm{ – }}\,{\rm{55}}\) is \(3\).

Q.5. The marks of the \(30\) students of the class in Mathematics are given below:  

Construct a grouped frequency distribution table by taking suitable intervals.
Ans:
The grouped frequency distribution table is given for the above-given data as follows:

Summary

In this article, we have studied the frequency distribution table and its types. This concept in statistics helps to find the data in simple tabular form, which is easy to understand. We have discussed the frequency, tally marks, which are the main features of constructing a frequency distribution table.

This article helps us understand one of the easy ways of representing data using this concept of statistics. The properties and applications of the frequency distribution table help us explore the data features easily.

FAQs on Frequency Distribution Table

Q.1: How do you describe a frequency distribution table?
Ans: In statistics, frequency distribution tables are one of the best ways to represent the data. The frequency distribution table is used to analyse the data of a larger set.

Q.2: How do you calculate frequency distribution?
Ans: To make the frequency distribution table,
1. Write the categories in the first column.
2. Tally, the score of the category of the given data in the second column
3. Count the tally and write the frequency of each category in the third column

Q.3: What are the differences between the frequency table and the frequency distribution table?
Ans: The frequency table is a tabular method where each part of the data is assigned to its corresponding frequency. In comparison, a frequency distribution is generally the graphical representation of the frequency table.

Q.4: What are the \({\rm{3}}\) types of frequency distribution?
Ans: The \({\rm{3}}\) types are
1. Ungrouped frequency distribution
2. Grouped frequency distribution
3. Cumulative frequency distribution

Q.5: What is a frequency distribution?
Ans: In statistics, the frequency distribution represents the data in a tabular or graphical manner, which shows the frequency of all the given data.

We hope you find this article on Frequency Distribution Table helpful. In case of any queries, you can reach back to us in the comments section, and we will try to solve them. 

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