The frequency distribution is a topic in statistics related to data handling. The term frequency is how often something occurs and distribution means dividing and sharing something. Get the examples, the definition of frequency distribution, and learn about the frequency distribution table. Find the solved examples that help you to understand the concept clearly.
Frequency Distribution Definition
The frequency distribution describes how frequencies are distributed over the data. It is a representation either in tabular or graphical format, that displays the number of observations within the given interval.
The terms of the frequency distribution are listed here:
- Presentation of Data:Â After collecting the data, shortly in the tabular form in order to study its features, such arrangement is known as the data presentation.
- Observation:Â Each entry collected as a numerical number in the given data is called the observation.
- Frequency:Â The number of times a particular observation repeat is known as the frequency.
- Frequency Distribution Table:Â It is one form of representation of the data. It contains the observations and how many times those observations occur.
Steps to Draw a Frequency Distribution Table
- Arrange the given data in ascending order.
- And find the frequency of each data value.
- Take the data value and frequency as the two columns in the table.
- Write each data value frequency in the table.
Get more useful information regarding the data handling such as the types of data, definition, and terms used in the data handling.
Example of Frequency Distribution
Example 1.
Suppose the runs scored by the 11 players of the Indian cricket team in a match are given as follows:
25, 65, 03,12, 35, 46, 67, 56, 00, 31, 17
State the frequency of each player?
Solution:
Given that,
Runs scored by the 11 players of the cricket team in a match are 25, 65, 03,12, 35, 46, 67, 56, 00, 31, 17
Arranging the data in ascending order, we get the observations as
00, 03, 12, 17, 25, 31, 35, 46, 56, 65, 67
We find that Each value has occurred only once.
We may represent the above data in a tabular form, showing the frequency of each observation. This representation is called a frequency distribution.
Frequency Distribution Table
| Player | Runs Scored By Each Player (Frequency) |
|---|---|
| Player 1 | 00 |
| Player 2 | 03 |
| Player 3 | 12 |
| Player 4 | 17 |
| Player 5 | 25 |
| Player 6 | 31 |
| Player 7 | 35 |
| Player 8 | 46 |
| Player 9 | 56 |
| Player 10 | 65 |
| Player 11 | 67 |
| Overall score in the match | 357 |
Example 2.
In a quiz, the marks obtained by 20 students out of 30 are given as:
12, 15, 15, 29, 30, 21, 30, 30, 15, 17, 19, 15, 20, 20, 16, 21, 23, 24, 23, 21
State the frequency of each student.
Solution:
Given that,
Marks obtained by 20 students in quiz out of 30 are 12, 15, 15, 29, 30, 21, 30, 30, 15, 17, 19, 15, 20, 20, 16, 21, 23, 24, 23, 21
Arranging the data in ascending order, we get the marks list as
12, 15, 15, 15, 15, 16, 17, 19, 20, 20, 21, 21, 21, 23, 23, 24, 29, 30, 30, 30
The highest marks obtained student is 30, the lowest marks are 12, the range is 30 – 12 = 18
From the data, we find that
12 marks scored by one student,
15 marks scored by 4 students,
16, 17, 19 marks scored by one student,
20 marks scored by 2 students,
21 marks scored by 3 students,
23 marks scored by 2 students,
24, 29 marks scored by one student,
30 marks scored by 3 students,
We may represent the above data in a tabular form, showing the frequency of each observation. The number of times data occurs in a data set is known as the frequency of data
This tabular form of representation is called a frequency distribution.
| Marks obtained in the quiz | Number of students(Frequency) |
|---|---|
| 12 | 1 |
| 15 | 4 |
| 16 | 1 |
| 17 | 1 |
| 19 | 1 |
| 20 | 2 |
| 21 | 3 |
| 23 | 2 |
| 24 | 1 |
| 29 | 1 |
| 30 | 3 |
| Total | 20 |
Example 3.
The numbers of newspapers sold at a local shop over the 10 days are:
22, 20, 18, 23, 20, 25, 22, 20, 18, 20
State the frequency.
Solution:
Given that,
The total number of newspapers sold at the local shop past 10 days are 22, 20, 18, 23, 20, 25, 22, 20, 18, 20
By arranging the newspapers numbers in ascending order is 18, 18, 20, 20, 20, 20, 22, 22, 23, 25
The frequency table for the papers sold is given here:
| Paper Sold | Frequency |
|---|---|
| 18 | 2 |
| 20 | 4 |
| 22 | 2 |
| 23 | 1 |
| 25 | 1 |
| Total | 10 |