 In Mathematics, Frequency is the number that reveals how often a specific item occurs in the data set. For example, two kids like the black color then the frequency is two. But making frequency for the large datasets is not possible sometimes so frequency distribution comes in the frame and helps everyone to solve the huge dataset problems. Learn more about Frequency Distribution its definition, formula, types, table, examples from this page and excel in solving all types of questions in exams.

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What is Frequency Distribution in Statistics?

The representation of data that shows the number of observations that occurred within the given interval is called frequency distribution in statistics. It can be represented in graphical or tabular form for easy understanding to kids. Especially, Frequency distributions help in summarizing large data sets and allocating probabilities.

A few data examples are test scores of students, points scored in a basketball match, temperatures of various towns, etc.

For Example: Let’s consider the following scores of 10 students in the Math MCQ exam: 10, 15, 20, 15, 17, 19, 12, 10, 20, 15. Let’s represent this data in frequency distribution and calculate the number of students who scored the same marks.

 Math MCQ Exam Scores No.of Students 10 12 15 17 19 20 2 1 3 1 1 2

Now, you can see the organized data under two columns ie., MCQ Exam Scores and No.of students. By this, students can easily understand the given data and find out the number of students who obtained the same marks. Hence, frequency distribution in statistics aids everyone to arrange the data in an easy manner to grasp its benefits in one look.

Frequency Distribution Formula

Whenever multiple classes are included in the given data, finding the distribution for ungrouped data will be tough. In such instances, the number of classes can be calculated by using the following frequency distribution formula:

C (no. of classes) = 1 + 3.3 logn where(log is base 10) or alternatively the square root of frequency distribution formula is written as:

C = √n, where n is the total no. of observations of the data that has been distributed.

Types of Frequency Distribution

We can see four different frequency distribution types in statistics and they are illustrated below:

1. Relative frequency distribution: It represents the proportion of the total number of observations connected with each category.

2. Cumulative frequency distribution: The sum of all frequencies in the frequency distribution is called cumulative frequency distribution. The total sum of all frequencies is the last cumulative frequency.

3. Classified or Grouped frequency distribution: The data is organized or separated into groups called class intervals. Then, the frequency of data of each class interval is calculated and put down in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.

For Example:

 Marks Obtained 4 20 30 39 40 45 49 50 65 70 79 80 90 Total Number of Students 3 7 7 1 3 5 1 9 2 5 1 2 4 50

4. Unclassified or Ungrouped frequency distribution: Representing the frequency of data in each separated data value instead of data value groups is called ungrouped frequency distribution. Look at the below example table to understand it better.

For Example:

 Marks Obtained From 0 to under 20 From 20 to under 40 From 40 to under 60 From 60 to under 80 From 80 to under 100 Number of Students 3 15 (i.e., 7 + 7 + 1) 18 (i.e., 3 + 5 + 1 + 9) 8 (i.e., 2 + 1) 6 (i.e., 2 + 4)

How to Calculate Frequency Distribution in Statistics?

By following some simple steps, we can easily find the frequency distribution in statistics:

1. At first, we have to read the given data properly then make a frequency chart.
2. Initially, take the categories in the first column.
3. Next, use the tally marks in the second column.
4. Later, count the tally to note down the frequency of each category in the third column.
5. Finally, we can find the frequency distribution of the given data set.

Frequency Distribution Table

It is a chart that displays the frequency of each item in a data set. To understand it in a better way, let’s take an instance and grasp how to create a frequency distribution table using tally marks.

Example: A Glass bowl contains various colors of beads ie., red, green, blue, black, red, green, blue, yellow, red, red, green, green, green, yellow, red, green, yellow. To find the exact number of beads of each color, we use the frequency distribution table.

Solution:

Firstly, we have to classify the beads into categories. Then, we go for the easiest method of finding the number of beads of each color ie., using tally marks. Now, take the beads one after one and enter the tally marks in the particular row and column. Finally, note down the frequency for each item in the table as shown below: Hence, the obtained table is called a Frequency Distribution Table.

Frequency Distribution Example Problems with Solutions

Example 1:
A blood donation camp is conducted by the school and 30 students’ blood groups were recorded as A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table?
Solution:
The given data can be shown in a frequency distribution table as follow:

Blood Group Number of students
A 9
B 6
AB 3
O 12
Total 30

Example 2:
Let’s consider a car survey where people were asked how many cars were registered to their households in each of 15 homes. The outcomes were like this 1, 3, 5, 2, 3, 0, 4, 2, 5, 1, 3, 2, 6, 3, 3. Now, find the maximum number of cars registered by household and also represent this data in Frequency Distribution Table.
Solution:
Firstly, arrange the data along with their frequencies in the frequency distribution table.
Divide the number of cars (x) into intervals, and then count the number of results in each interval (frequency).

 Number of Cars Frequency 0 1 1 2 2 3 3 4 4 1 5 2 6 1 Total 15

Thus, from the above frequency distribution table, it is clear that the 4 household has 3 cars.