## 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.## Question

Construct a cumulative grouped frequency table for the numbers below.## Step-by-Step:

## 1

Construct a table with four columns:

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

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

## 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.## 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. 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.

## 4

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

**Frequency**column.## 5

Complete the

**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.

## Answer:

The cumulative grouped frequency table is complete when all the cumulative frequencies have been entered:## You might also like...

statisticsunderstanding cumulative grouped frequency tablesunderstanding bar chartsreading from a bar chart

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## 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?