# How to Make a Cumulative Frequency Table (Mathematics Lesson)

# Making a Cumulative Grouped Frequency Table

A cumulative grouped 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:

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

# How to Make a Cumulative Grouped Frequency Table

Making a cumulative grouped frequency table is easy.#### An Example Question

Construct a cumulative grouped frequency table for the numbers below.Step 1

Before we make a cumulative grouped frequency table, we need to make a grouped frequency table (the first three columns).

Read about how to make a grouped frequency table

Step 2

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

Step 3

**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. It belongs in the
**6 - 10**group. Cross it out and put a tally mark in the**Tally**column in the**6 - 10**row.

- Continue until all numbers have been crossed out and had tally marks placed in the
**Tally**column.

Step 4

**Frequency**column.

Step 5

**Cumulative frequency**column. The cumulative frequency in each row is found by adding all the entries in the

**Frequency**column from the top row to that row.

- The cumulative frequency in the first row is equal to the frequency:

- The cumulative frequency in the second row is found by adding the frequency in this row to all the frequencies above:

**Note:**It is also found by adding the frequency in this row to the cumulative frequency above. - The cumulative frequency in the third row is found by adding the frequency in this row to all the frequencies above:

**Note:**It is also found by adding the frequency in this row to the cumulative frequency above. - The cumulative grouped frequency table is complete when all the cumulative frequencies have been entered:

# A Real Example of How to Make a Cumulative Grouped Frequency Table

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

# What Is a Cumulative Grouped Frequency Table?

A cumulative grouped frequency table is a grouped frequency table with a running total of the frequencies.A grouped frequency table is a frequency table where the numbers are grouped together.

It shows you how often numbers within each group appear 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.

##### Top Tip

# Quick Check

The final entry in the**Cumulative frequency**column must equal the total of the

**Frequency**column.

Add up the

**Frequency**column to see if it is the same as the last number you write in the

**Cumulative frequency**column:

# The Cumulative Frequency Is Increasing

The numbers in the**Cumulative frequency**column must increase as you go down the rows.

This is because each time you go down a row, you add another frequency to the running total, so it must get larger.

Sometimes a the cumulative frequency will stay the same. What must the frequency be in that row?

##### Note

# 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 numbers in the 1 - 5 group. Then all the numbers in the 6 - 10 group etc.
- Order the numbers and group like numbers together.