Types of Frequency Distribution: Definition, and Examples

Types of Frequency Distribution: The frequency distribution in statistics provides details on the frequency of unique values spread out throughout a certain time period or interval in a list, table, or graphical representation. There are two categories of frequency distribution: grouped and ungrouped. Data is a collection of figures or values that must be organised in a useful way. Let’s study the frequency distribution of the data.

The four different forms of frequency distributions are ungrouped frequency distributions, grouped frequency distributions, cumulative frequency distributions, and relative frequency distributions. We’ll go deeper into frequency distribution and its numerous types in the below article.

Types of Frequency Distribution: Definition

A frequency distribution is a graphical or tabular representation of data that shows the number of observations within a given value. The collected information is categorised in table form utilising frequency distribution. Students’ scores, temperatures in different towns, points scored in a volleyball match, and so on could be included in the data.

After collecting information, we should display it in a significant way for greater understanding. Organise the data such that all of its properties are represented in a table. It is known as frequency distribution.
Let’s consider an example to understand this better. The following are the scores of \(12\) students in the mathematics quiz released by Mr Asit \(14, 16, 17, 20, 14, 16, 20, 17, 17, 14, 14, 20\).
Let’s put this data into a frequency distribution to see how many children receive the same score.

All of the collected data is arranged under the quiz marks and number of students column, as can be seen. It makes it easy to understand the information provided, and we can see the number of students that got the same score. As a result, frequency distribution in statistics helps us arrange data to make it simple to understand its characteristics at a glance.

Types of Frequency Distribution in Statistics

In statistics, there are four types of frequency distributions, which are discussed below:

1. Ungrouped frequency distributions: Instead of sets of data values, it presents the frequency of an item in each particular data value.
2. Grouped frequency distributions: The data is organised and grouped into groups called class intervals in this type. In a frequency distribution table, the frequency of data 
   belonging to each class interval is represented. The grouped frequency table shows the frequency distribution in class intervals.
3. Relative frequency distributions: It indicates what percentage of the total number of observations each category belongs to.
4. Cumulative frequency distributions: A frequency distribution is the sum of the first frequency and all frequencies below it. We must add each value to the next, then add the sum to the next, and so on until the last value is reached. The whole sum of all frequencies will be the last cumulative frequency.

Frequency Distribution Table

A frequency distribution table is a table that represents how many each item in a data set occurs. To see how to build a frequency distribution table with tally marks, examine the following example. 
Red, blue, pink, red, green, red, blue, pink, red, blue, blue, yellow, pink, red, red, blue, yellow.

We must first classify the beads to get the exact quantity of beads of each colour. Applying tally marks is an easy approach to determining the number of beads of each colour. Please pick up the beads one by one and put them in a suitable row and column. Then, for each item in the table, indicate the frequency.

Colours	Tally Marks	Frequency
Red		\(6\)
Blue		\(5\)
Green		\(1\)
Pink		\(3\)
Yellow		\(2\)

As a result, the table is called a frequency distribution table.

Types of Frequency Distribution Table

There are two types of frequency distribution tables.

Ungrouped frequency distribution table: We don’t make class intervals in the ungrouped frequency distribution table; instead, we write the exact frequency of individual data.

Grouped frequency distribution table: To arrange a large number of observations or data, we use grouped frequency distribution table. We form class intervals to tally the frequency for the data that belongs to that particular class interval.

Frequency Distribution on Graphs

Another way to represent data in the form of graphs is by using a frequency distribution graph. The graphs make this easy to understand the collected data. The following are the details of a graphical representation of a frequency distribution.
(i) Bar Graph: Bar graphs are graphs that use rectangular bars of constant width with equal spacing among them to show data.

(ii) Histograms: Histograms are graphical representations of data that use rectangular bars of different heights. There is no space between the rectangular bars in a histogram.

(iii) Pie chart: A pie chart is a graph that uses a circular chart to display data visually. It records data in a circular pattern and then divides it into sectors, each showing a part of the total data.

(iv) Frequency Polygon: In a histogram, a frequency polygon is formed by joining the mid-points of the bars.

Solved Examples – Types of Frequency Distribution Types

Q.1. There are \(25\) students in a class. The teacher, Ms Jaya, asked the students to tell their favourite subject. The results are as follows – Mathematics, English, Science, Science, Mathematics, Science, English, Art, Mathematics, Mathematics, Science, Art, Art, Science, Mathematics, Art, Mathematics, English, English, Mathematics, Art, Mathematics, Science, Science, English. Represent this data in the form of frequency distribution and identify the most-liked subject?
Ans: A total of \(25\) students have selected their preferred subjects. Let’s use tally marks to indicate this data. The tally marks show the frequency of each subject.

Subject	Tally Marks	Number of students
Mathematics		8
Science		7
English		5
Art		5

Hence, the most liked subject is Mathematics.

Q.2. The following is the distribution for the age of students in a Gurukula International school:

Calculate the class limits of the fourth class?
Ans: The class limits of the fourth class, i.e. \(15-20\), are \(15\) is the lower limit (lower limit), and \(20\) is the upper limit.

Q.3. Vishu noted her results after her ten throws of a fair dice as follows: \(4, 6, 1, 2, 2, 5, 6, 6, 5, 4\). Create the frequency distribution of the given data using the frequency distribution formula.
Ans: Frequency distribution table is given below,

Q.4. Suppose we make a survey of 18 families of a locality and find out the number of children in each family. Let the observations be \(3, 1, 1, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 1, 1, 3, 2, 2\). State the frequency of each observation.
Ans: The frequency distribution table is given below,

Number of children	Tally marks	Frequency
\(1\)		\(6\)
\(2\)		\(8\)
\(3\)		\(4\)
	Total	\(18\)

Q.5. The research was done in \(22\) homes in Karnataka. People were asked how many bikes did they own? The results were: \(1, 4, 3, 0, 5, 1, 2, 2, 1, 5, 2, 3, 2, 2, 0, 1, 2, 0, 3, 2, 1, 4\). Present this data in Frequency Distribution Table.
Ans: Represented the data in a frequency distribution table is given below by,

Summary

A frequency distribution is a table that shows how often certain outcomes occur in a sample. The table describes the distribution of values in the sample, including the frequency or count of values within that group or interval in each entry. This article includes the definition of frequency distribution, types of frequency distribution, the meaning of frequency distribution table, types of frequency distribution table, and examples of frequency distribution.

Learn About Frequency Distribution Table

FAQs Regarding Types of Frequency Distribution

Below are the frequently asked questions about the types of Frequency Distribution

Q.1. What is frequency distribution in statistics, for example?
Ans: A graph or data set organised to show the frequency of each possible outcome of a repeatable event observed many times is called a frequency distribution in statistics. Election results and percentile test scores are simple examples. A histogram or pie chart could be used to illustrate a frequency distribution.

Q.2. What are the advantages of frequency distribution?
Ans: Frequency distributions have the advantage of displaying raw data in an organised, easy-to-read format. The scores that occur the most frequently can be easily identified.

Q.3. What are the four types of frequency distributions?
Ans: Four types of frequency distributions are,
1. Ungrouped frequency distributions
2. Grouped frequency distributions
3. Cumulative frequency distributions
4. Relative frequency distributions 

Q.4. What is frequency distribution in statistics, for example?
Ans: A graph or data set organised to show the frequency of each possible outcome of a repeatable event observed many times is called a frequency distribution in statistics. Election results and percentile test scores are simple examples. A histogram or pie chart could be used to illustrate a frequency distribution.

Q.5. What is the frequency distribution formula?
Ans: The frequency distribution formula is the frequency distribution in tabular or graphic form. The frequency distribution is a tabular representation that illustrates each data point and its frequency. One of the various ways of organising the data is to use the frequency distribution formula.

We hope this detailed article on frequency distribution and its types helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!