You have been learning all about the different ways to display data. In this lesson, you will learn about frequency tables and histograms. Let’s start by looking at frequency tables.

What is a frequency table?

A frequency table is another way of summarizing data. A frequency table depicts the number of times a data value occurs.

A frequency table is created by making a table with three separate columns. One column is designated for intervals. The amount of intervals is determined by the range in data values. If the range in data values is not that great, the intervals will be small. If the range in data values is great, the intervals will be larger. It is important that the intervals are of equal size and do not overlap.

Another column is created for tallied results. This is where you tally the number of times you see a data value from each interval.

In the last column, add the tally marks to determine the frequency results.

Let’s look at how we can apply this information with an example.

Example 1

Twenty people were asked to state the number of hours they sleep each night. The results of the survey are listed below. Create a frequency table to display the data.

7, 8, 6, 9, 10, 12, 5, 7, 8, 9, 10, 11, 12, 7, 6, 7, 8, 10, 11, 9

Step 1: Make a table with three separate columns.

• Intervals
• Tallied results
• Frequency results

In this case, there is not a wide range in data values, therefore the intervals will be displayed by ones.

Step 2: Looking at the data, tally the number of times a data value occurs.

Step 3: Add the tally marks to record the frequency.

Number of Hours Slept	Tally	Frequency
5	I	1
6	I I	2
7	I I I I	4
8	I I I	3
9	I I I	3
10	I I I	3
11	I I	2
12	I I	2

Now you can see how arranging the data in this way makes it much easier to follow.

Example 2

The data below depicts the amount of time (in minutes) 20 middle school students spent on the computer each day. Arrange the data on a frequency table.

10, 32, 8, 55, 5, 0, 30, 20, 25, 45, 40, 60, 45, 15, 5, 56, 47, 12, 15, 20

Step 1: Make a table with three separate columns.

• Intervals
• Tallied results
• Frequency results

In this case, there is not a wide range in data values, therefore the intervals will be displayed by ones.

Step 2: Looking at the data, tally the number of times a data value occurs.

Step 3: Add the tally marks to record the frequency.

Number of Minutes on the Computer	Tally	Frequency
0 – 5	I I I	3
6 – 10	I I	2
11 – 15	I I I	3
16 – 20	I I	2
21 – 25	I	1
26 – 30	I	1
31 – 35	I	1
36 – 40	I	1
41 – 45	I I	2
46 – 50	I	1
51 – 55	I	1
56 – 60	I I	2

Once again, the tally marks in the frequency table can give you a clear picture of the data.