How to Make a Frequency Table (Mathematics Lesson)
Making a Frequency TableA frequency table is a great way to present a lot of data.
Imagine a teacher wanted an easy way to present the test scores of their mathematics class:
How to Make a Frequency TableMaking a frequency table is easy.
An Example QuestionConstruct a frequency table for the numbers below.
- The first number is 8. Cross it out and put a tally mark in the Tally column in the 8 row.
- The second number is 10. Cross it out and put a tally mark in the Tally column in the 10 row.
- Continue until all numbers have been crossed out and had tally marks placed in the Tally column.
This is the frequency table for the set of numbers given in the question.
A Real Example of How to Make a Frequency TableThe slider below gives another example of making a frequency table.
Finding Averages from a Frequency TableThe frequency table can be used to find the average of a set of numbers.
A frequency table can be used to find: Read more about how to find the mean from a frequency table.
Read more about how to find the median from a frequency table.
Read more about how to find the mode from a frequency table.
What Is a Frequency Table?A frequency table shows how often (how frequently) each number appears in a list of numbers.
What Are Tally Marks?Tally marks are a way of helping you to count, especially when you have to count a large set of numbers.
A vertical line is made for the first four numbers:
To make five, a diagonal bar is drawn across the four vertical lines:
After five, single bars are added again:
Once ten is reached, two groups of five tally marks are used:
Finally, it is easy to count the total number of tally marks. For example, consider the tally marks below:
Count up the groups of five tally marks in fives:
Finally add, the number of single marks:
There are 22 tally marks.
Quick CheckWhen there are a large number of numbers to put into a frequency table, it is easy to go wrong counting them.
Crossing the numbers off as you enter them into the Tally column is one way of ensuring you check each number once only.
Another useful check is to add all the numbers in the Frequency column. They should sum to the number of numbers there were to begin with.
For example, if there are six numbers:
You obtain the following frequency table:
Summing up the frequency column gives
2 + 3 + 2 = 7This is not equal to the six numbers. This tells you that a mistake has been made. (In the example above, there is only one 3, not two).
Try to find the mistake or repeat the exercise.
Counting the NumbersIn the test scores example, the numbers have been counted one at a time going from left to right.
This is not the only way to do it. You could:
- Go through and count all the 5s. Then all the 6s. Then all the 7s etc.
- Order the numbers and group like numbers together.