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Making a Grouped Frequency Table

(KS3, Year 7)

Making a Grouped Frequency Table

A grouped frequency table is a great way to present a lot of data. Imagine a teacher collected the test scores of their mathematics class: grouped_frequency_table_test_scores

Depending on each student's test score, the teacher will assign a grade:

grouped frequency table scores to grades

How to Make a Grouped Frequency Table

Making a grouped frequency table is easy.

Question

Construct a grouped frequency table for the numbers below. make grouped frequency table example

Step-by-Step:

1

Construct a table with three columns:

make grouped frequency table step 1

2

In the Score column, write the groups of numbers. In our example, we will use the group of test scores assigned to the different grades.

make grouped frequency table step 2

3

Go through the set of numbers in the Question. For each number, see which of the group of numbers it belongs in. Cross it out and put a tally mark in the Tally column, in the row for that group of numbers.

The first number is 2. It belongs in the 1 - 5 group. Cross it out and put a tally mark in the Tally column in the 1 - 5 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.

4

For each row, count the tally marks. Write the number of tally marks in the Frequency column.

Answer:

We have made the grouped frequency table for the set of numbers given in the question. make_grouped_frequency_table_step_4

Lesson Slides

The slider below gives another example of making a grouped frequency table.

This page was written by Stephen Clarke.

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:

tally marks fives

Finally add, the number of single marks:

tally marks fives and two

There are 22 tally marks.

Top Tip

Quick Check

When 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:

tally marks grouped check sum

Summing up the frequency column gives

2 + 3 + 2 = 7

This is not equal to the six numbers. This tells you that a mistake has been made. (In the example above, there is only one number in the 11 - 15 group (15), not two). Try to find the mistake or repeat the exercise.

Counting the Numbers

In 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.

Find the way you find best to count the numbers without making mistakes. Feel free to try different ways until you find the one that suits you best.

Making a Grouped Frequency Table