Grouping of data plays an important role while dealing with a large amount of data. This information can also be displayed using a bar graph or pictograph. You can the grouping of data definition, solved examples in the below sections of this article. Furthermore, you will be familiar with the steps to draw a frequency distribution table for grouped data in the coming modules.
What is Meant by Grouping of Data?
When the number of observations is very large, we may divide the data into several groups, by using the grouping of data concept. The data formed by arranging the individual observations of a variable into groups, so that the frequency distribution table of these groups is a convenient way of summarizing the data. The advantages of grouping data are, it improves the accuracy/ efficiency of estimation, helps to focus on the important subpopulations, and ignores irrelevant ones.
Steps to Draw Frequency Distribution Table for Grouped Data
- From the given data, divide the data into some groups.
- Arrange the given observations in ascending order.
- Get the frequency of each observation.
- Write the frequency, group name in the frequency distribution table.
Get more useful information regarding the data handling such as the types of data, definition, and terms used in the data handling.
Solved Example Questions & Answers
Example 1.
The mass of 40 students in a class is given below. The measurement of the weight will be in kgs.
55, 70, 57, 73, 55, 59, 64, 72, 60, 48, 58, 54, 69, 51, 63, 78, 75, 64, 65, 57, 71, 78, 76, 62, 49, 66, 62, 76, 61, 63, 63, 76, 52, 76, 71, 61, 53, 56, 67, 71
State the frequency distribution table for the grouped data?
Solution:
Given that,
The weight of 40 students in a class are 55, 70, 57, 73, 55, 59, 64, 72, 60, 48, 58, 54, 69, 51, 63, 78, 75, 64, 65, 57, 71, 78, 76, 62, 49, 66, 62, 76, 61, 63, 63, 76, 52, 76, 71, 61, 53, 56, 67, 71
The ascending order of the students weight is 48, 49, 51, 52, 53, 54, 55, 55, 56, 57, 57, 58, 59, 60, 61, 61, 62, 62, 63, 63, 63, 64, 64, 65, 66, 67, 69, 70, 71, 71, 71, 72, 73, 75, 76, 76, 76, 76, 78, 78
The range = 78 – 48 = 30
The intervals should separate the scale into equal parts. We could choose intervals of 5. We then begin the scale with 45 and end with 79.
Frequency Distribution Table for Grouped Data is
| Mass in Kg | Frequency |
|---|---|
| 45 – 49 | 2 |
| 50 – 54 | 4 |
| 55 – 59 | 7 |
| 60 – 64 | 10 |
| 65 – 69 | 4 |
| 70 – 74 | 6 |
| 75 – 79 | 7 |
| Total | 40 |
Example 2.
The marks obtained by 40 students of Class VII in an examination are given below:
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23
State the frequency distribution table for the grouped data?
Solution:
Given data,
The marks scored by 40 students is 16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23
The ascending order of the marks is 0, 1, 2, 2, 3, 3, 5, 5, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 12, 12, 12, 13, 13, 13, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 21, 23, 23, 23, 24
Range is = 24 – 0 = 24
The intervals should separate the scale into equal parts. We could choose intervals of 5. We then begin the scale with 0 and end with 24.
Frequency Distribution Table for Grouped Data is
| Marks Scored | Number of Students (Frequency) |
|---|---|
| 0 – 4 | 6 |
| 5 – 9 | 10 |
| 10 – 14 | 8 |
| 15 – 19 | 9 |
| 20 – 24 | 7 |
| Total | 40 |
Example 3.
The height (in cms) of 35 persons are given below:
140, 125, 128, 126, 130, 134, 134, 146, 125, 140, 140, 127, 125, 137, 132, 134, 126, 128, 128, 129, 150, 151, 131, 138, 128, 129, 126, 127, 129, 130, 135, 132, 134, 140, 152
State the frequency distribution table for the grouped data.
Solution:
Given that,
The height of 35 persons are 140, 125, 128, 126, 130, 134, 134, 146, 125, 140, 140, 127, 125, 137, 132, 134, 126, 128, 128, 129, 150, 151, 131, 138, 128, 129, 126, 127, 129, 130, 135, 132, 134, 140, 152
Ascending order of the 35 persons height is 125, 125, 125, 126, 126, 126, 127, 127, 128, 128, 128, 128, 129, 129, 129, 130, 130, 131, 132, 132, 134, 134, 134, 134, 135, 137, 138, 140, 140, 140, 140, 146, 150, 151, 152
The range is 152 – 125 = 27
The intervals should separate the scale into equal parts. We could choose intervals of 4. We then begin the scale with 125 and end with 152.
Frequency Distribution Table for Grouped Data is
| Height (in Cms) | Number of Persons (Frequency) |
|---|---|
| 125 – 128 | 12 |
| 129 – 132 | 8 |
| 133 – 136 | 5 |
| 137 – 140 | 6 |
| 141 – 144 | 0 |
| 145 – 148 | 1 |
| 149 – 152 | 3 |
| Total | 35 |
Frequently Asked Questions on Grouping of Data
1. What is grouped and ungrouped data?
Grouped data is the data given in intervals whereas ungrouped data is the data without a frequency distribution.
2. What is a group of data called?
The frequency table is also called the grouped data. Grouped data is used in data analysis.
3. How can we convert ungrouped data to grouped data?
The first step of the conversion is to determine how many classes you have and find the range of data. And then divide the number of classes into groups.