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Making a Cumulative Frequency Table

(KS3, Year 7)

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

cumulative grouped frequency table scores to grades

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. make cumulative grouped frequency table example

Step-by-Step:

1

Construct a table with four columns:

make cumulative frequency table 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

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 cumulative 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. make cumulative grouped frequency table step 3 1
  • 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. make cumulative grouped frequency table step 3 2
  • Continue until all numbers have been crossed out and had tally marks placed in the Tally column. make cumulative grouped frequency table step 3 3

4

For each row, count the tally marks. Write the number of tally marks in the Frequency column. make_cumulative_grouped_frequency_table_step_4

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:

    make cumulative frequency table step 5 1
  • The cumulative frequency in the second row is found by adding the frequency in this row to all the frequencies above:

    make cumulative grouped frequency table step 5 2 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:

    make cumulative grouped frequency table step 5 3 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:

make cumulative grouped frequency table complete

Lesson Slides

The slider below gives another example of making a cumulative grouped frequency table.
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This page was written by Stephen Clarke.

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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:

tally 5 large After five, single bars are added again: Once ten is reached, two groups of five tally marks are used:

tally 10 large Finally, it is easy to count the total number of tally marks. For example, consider the tally marks below:

tally marks 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

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:

cumulative grouped frequency table check

The Cumulative Frequency Is Increasing

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

cumulative grouped frequency table increasing 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?