Constructing Frequency Distribution Tables: Nowadays, storing and recording data is very important for every firm and sector. A piece of information or any ideas or fact representations is called data. Data collection is maintaining every single piece of information like dates, scores, time, etc. Statistics is defined as the collection, presentation, analysis, organization, and interpretation of observations or data. In order to deal with huge data collection, statistics can be quite helpful.
Statistics and Statistical data collection can be presented in various types like tables, bar graphs, pie charts, histograms, frequency polygons, etc. Here, we are going to discuss data collection through a frequency distribution table and how to draw frequency distribution tables for grouped & ungrouped data with example problems and solutions.
Do Read:
- Frequency Distribution of Ungrouped and Grouped Data
- Class Limits
- Frequency of the Statistical Data
- Class Boundaries
What is Frequency Distribution Table in Statistics?
The general method of representing the organization of raw data of a quantitative variable is the frequency distribution table in statistics. By this table, we can easily find how different values of a variable are distributed and their corresponding frequencies. We can construct two frequency distribution tables in statistics. They are:
(i) Discrete frequency distribution table
(ii) Continuous frequency distribution table
How to Make a Frequency Distribution Table for Grouped Data?
A frequency distribution table can be constructed using tally marks for both discrete and continuous data values. Constructing frequency distribution tables for both discrete and continuous are different from each other.
Here we are learning how to make an ungrouped or raw or discrete frequency distribution table in simple steps along with examples.
For instance, let’s consider the result of a survey from the household on finding out how many bikes they own. The results are 3, 0, 1, 4, 4, 1, 2, 0, 2, 2, 0, 2, 0, 1, 3 now make the table to understand the data easily. Follow the steps carefully and draw a frequency table:
Step 1: Firstly, draw a table with three columns. Now, take the categories in one column (number of bikes):
| Number of bikes (x) | Tally | Frequency (f) |
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
Step 2: In this step, we will use the tally marks approach and tally the numbers in each category. From the above example, the number zero appears four times in the list, so place four tally marks “||||” in the respective row and column.
| Number of bikes (x) | Tally | Frequency (f) |
| 0 | |||| | |
| 1 | ||| | |
| 2 | |||| | |
| 3 | || | |
| 4 | || |
Step 3: At last, count the tally marks and write down the frequency in the third column. The total tallies is the frequency value placed in the final column. Here, you have four tally marks for 0, thus put 4 in the last column.
| Number of bikes (x) | Tally | Frequency (f) |
| 0 | |||| | 4 |
| 1 | ||| | 3 |
| 2 | |||| | 4 |
| 3 | || | 2 |
| 4 | || | 2 |
How to Construct a Frequency Distribution Table using Class Limits? (Simple Steps for Ungrouped Data)
Follow the below easy steps to draw a frequency distribution table:
Step 1: Understand how many classes (categories) you require. Follow some of these basic rules about how many classes to select.
- Choose between 5 and 20 classes.
- Ensure that you have a few items in each class. For instance, in case you have 20 items, pick 5 classes (4 items per category), not 20 classes (that would give you only one item per category).
Step 2: Subtract the smallest data value from the highest one and find the range of the statistical data.
Step 3: Now, divide the result get in step 2 by the number of classes you picked in step 1.
Step 4: If you get a decimal result, round the number to the whole number to obtain the class width.
Step 5: Take the least value from the data set.
Step 6: Now, add the class width to step 5 for finding the next lower class limit.
Step 7: Keep on adding your class width to the minimum data values one by one till you create the number of classes you picked in step 1.
Step 8: Note down the upper-class limits. These are the maximum values that can be in the category, thus in such cases, you may subtract 1 from the class width and add that to the least data values.
Step 9: Add a second column for the number of items in each class, and name the column with suited headings.
Step 10: Count the items in each class and place the total in the second column. Thus, the frequency distribution table including classes can be constructed in an easy way.
Check out the detailed explanation of constructing frequency distribution tables using tally marks and classes from the below example problems and solve them on a daily basis for getting a good grip on the concept of how to draw frequency distribution tables.
Steps in Constructing Frequency Distribution Table Example Problems with Solutions PDF
Example 1:
Construct the frequency distribution table for the following runs scored by the 11 players of the Indian cricket team in the match. The scores are 40, 65, 70, 85, 00, 20, 35, 55, 70, 65, 70.
Solution:
The given data is in raw data and this type can represent in the tabular form to understand the data easily and more conveniently.
Thus, the data can be represented in tabular form ie., Frequency Distribution Table (Ungrouped) as follows:
| No.of Runs Scored | Tally | Frequency |
| 00 | | | 1 |
| 20 | | | 1 |
| 35 | | | 1 |
| 40 | | | 1 |
| 55 | | | 1 |
| 65 | || | 2 |
| 70 | ||| | 3 |
| 85 | | | 1 |
| Total: 11 |
Example 2:
The heights of 45 students, measured to the nearest centimetres, have been found to be as follows:
161, 150, 154, 165, 168, 161, 154, 162, 150, 151, 164, 171, 165, 158, 154, 156, 160, 170, 153, 159, 161, 170, 162, 165, 166, 168, 165, 164, 154, 152, 153, 156, 158, 162, 160, 161, 166, 161, 159, 162, 159, 158, 153, 154, 159.
Explain the data given above by a grouped frequency distribution table, taking the class intervals as 155 – 160, 160 – 165, etc.
Solution:
(i) Let us make the grouped frequency distribution table with classes:
150 – 155, 155 – 160, 160 – 165, 165 – 170, 170 – 175
Class intervals and the corresponding frequencies are tabulated as:
| Class intervals | Frequency | Corresponding data values |
| 150 – 155 | 12 | 150, 150, 151, 152, 153, 153, 153, 154, 154, 154, 154, 154 |
| 155 – 160 | 9 | 156, 156, 158, 158, 158, 159, 159, 159, 159 |
| 160 – 165 | 13 | 160, 160, 161, 161, 161, 161, 161, 162, 162, 162, 162, 164, 164 |
| 165 – 170 | 8 | 165, 165, 165, 165, 166, 166, 168, 168 |
| 170 – 175 | 3 | 170, 170, 171 |
| Total | 45 |
Example 3:
Lasya and Tara have a set of playing cards with numbers from 1 to 10. They pick a random card and record the number that comes up. They remain the same process at least 10 times. They get the values like 4, 8, 4, 2, 3, 7, 3, 4, 5, 9. Draw a frequency table to organize the data conveniently.
Solution:
Given values are is 4, 8, 4, 2, 3, 7, 3, 4, 5, 9 out of 1 to 10.
Now, construct the frequency table for ungrouped data:
| Values | Frequency |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 3 | 2 |
| 4 | 3 |
| 5 | 1 |
| 6 | 0 |
| 7 | 1 |
| 8 | 1 |
| 9 | 1 |
| 10 | 0 |
| Total | 10 |