What is a Frequency Table?
The definition of the word “frequency” is how often something occurs.
So, a frequency table shows how many occurrences have taken place.
You may need to count items or events to determine their frequency.
The counted items are also called data.
The data is placed into groups or categories.
Frequency tables usually have two or more columns.
The first column shows the category and the second column shows the frequency.
You may also see three column frequency tables.
In three column tables, the first column shows the category, the second column shows the tally or count, and the third column shows the frequency.
Example of a Frequency Table
Suppose that you have to keep track of the amount of rain in your town each day for two weeks.
At the end of the two weeks, you have recorded the following amounts in inches per day:
- Day 1: 2.1
- Day 2: 1.0
- Day 3: 0.5
- Day 4: 0.0
- Day 5: 0.2
- Day 6: 0.1
- Day 7: 1.4
- Day 8: 2.0
- Day 9: 2.2
- Day 10: 1.1
- Day 11: 0.8
- Day 12: 0.7
- Day 13: 0.6
- Day 14: 1.8
To make a frequency table, you have to sort your results into groups.
So, this type of table is called a grouped frequency table.
|
Rainfall in My Town for 2 Weeks |
|||
| Amount in inches | Tally | Frequency | |
| 0 to 0.5 | |||| | 4 | |
| 0.6 to 1.0 | |||| | 4 | |
| 1.1 to 1.5 | || | 2 | |
| 1.6 to 2.0 | || | 2 | |
| 2.1 to 2.5 | || | 2 | |
In other words, there were 4 days when the amount of rainfall was between 0 and 0.5 inches.
There were 4 days when the amount of rainfall was between 0.6 and 1.0 inches, and so on.
Frequency Table – Exercise
Now look at the following data and then complete the frequency table.
The answer is provided after the exercise.
Exercise: A basketball team records the number of points it scores in each game of the season. Complete the frequency table for the following data.
|
Basketball Games This Season |
|||
| Points | Tally | Frequency | |
| 0 to 25 | |||
| 26 to 50 | |||
| 51 to 75 | |||
| More than 75 | |||
- Game 1: 25
- Game 2: 36
- Game 3: 55
- Game 4: 24
- Game 5: 70
- Game 6: 48
- Game 7: 59
- Game 8: 76
- Game 9: 32
- Game 10: 41
Answer to Frequency Table Exercise
Remember to count up the items for each group in the “tally” column, and then write the number in the “frequency” column.
|
Basketball Games This Season |
|||
| Points | Tally | Frequency | |
| 0 to 25 | || | 2 | |
| 26 to 50 | |||| | 4 | |
| 51 to 75 | ||| | 3 | |
| More than 75 | | | 1 | |
Frequency Tables for Continuous Data
In many cases, you will need to think carefully when setting up categories for your data.
You need to be sure that your categories will include the results for all of your data.
Consider the following example.
Example: Eight students take part in a race. Their times in seconds are shown below.
- Student 1: 41.25
- Student 2: 36.29
- Student 3: 29.14
- Student 4: 41.38
- Student 5: 35.92
- Student 6: 20.99
- Student 7: 37.02
- Student 8: 38.64
|
Summary of Race Results in Seconds |
|||
| Seconds | Tally | Frequency | |
| 0 to 20 | |||
| 21 to 35 | |||
| 36 to 40 | |||
| 41 to 65 | |||
If we try to use the above table for our results, we will not be able to place the results for student 5 and student 6 into any of the above categories.
That is because student 5’s result of 35.92 seconds does not fit into either the “21 to 35 seconds” category or the “36 to 40 seconds” category.
In addition, student 6’s result of 20.99 seconds does not fit into either the “0 to 20 seconds” category or the “21 to 35 seconds” category.
Using Inequalities in Frequency Tables
We can solve this problem by using inequalities to ensure that our categories are continuous.
Exercise: Fill in the frequency table below. Variable “S” represents the result in seconds. The students’ results are provided again for ease of reference.
|
Summary of Race Results in Seconds |
|||
| Seconds | Tally | Frequency | |
| 0 ≤ S < 20 | |||
| 20 ≤ S < 35 | |||
| 35 ≤ S < 40 | |||
| 40 ≤ S < 65 | |||
- Student 1: 41.25
- Student 2: 36.29
- Student 3: 29.14
- Student 4: 41.38
- Student 5: 35.92
- Student 6: 20.99
- Student 7: 37.02
- Student 8: 38.64
When you have completed the table, check your answer below.
Answer to Continuous Frequency Table Exercise
|
Summary of Race Results in Seconds |
|||
| Seconds | Tally | Frequency | |
| 0 ≤ S < 20 | 0 | ||
| 20 ≤ S < 35 | || | 2 | |
| 35 ≤ S < 40 | |||| | 4 | |
| 40 ≤ S < 65 | || | 2 | |
Notice how student 5’s result of 35.92 seconds now fits into the “35 ≤ S < 40 seconds” category.
Student 6’s result of 20.99 seconds fits into the “20 ≤ S < 35 seconds” category.
When you have completed the exercises on this page, you may also want to look at our separate exercise on inequalities.