## Making a Frequency Table

A 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 Table

Making a frequency table is easy.## Question

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

## 1

Construct a table with three columns:

## 2

In the

**Score**column, write each number that appears in the set of numbers down the column, from the smallest to largest.## 3

Go through the set of numbers in the

**Question**. For each number, cross it out and put a tally mark in the**Tally**column, in the row for that number.- 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.

## 4

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

**Frequency**column.## Answer:

We have made the frequency table for the set of numbers given in the question.## You might also like...

statisticsunderstanding frequency tablesfinding the mean from a frequency tablefinding the median from a frequency table

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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

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:

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 3, 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.