# How to Get the Mean Average From a Frequency Table

## How To Work Out The Mean From A Frequency Table Video

The mean average from an ungrouped frequency table can be found by following these three simple steps:

Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply the first two columns together (the first column of the frequency table is usually referred to as x).

Step 2. Find the totals of the frequency column (2^{nd} column) and the xf column (3^{rd} column).

Step 3. Finally, divide the total of the xf column by the total of the frequency column. This will give you the mean average.

Let’s take a look at an example:

Twenty students took a math test and their results were recorded in the following frequency table (the test was marked out of 10). Work out the mean test score from the frequency table.

To answer this question you just to need to follow the 3 steps above:

Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply the first two columns together.

Step 2. Find the totals of the frequency column (2^{nd} column) and the xf column (3^{rd} column).

The total of the frequency column is 20.

The total of the fx column is 162

Step 3. Finally, divide the total of the xf column by the total of the frequency column. This will give you the mean average.

162 ÷ 20 = 8.1

So the mean average from the frequency table was 8.1 marks out of 10.

Let’s look at one more example of working out the mean average from a frequency table. This time you need to work out the mean race time in minutes of these 13 athletes who took part in a race.

Like the last example all you need to do is follow the 3 steps above to give the mean race time of these runners:

Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply the first two columns together.

Step 2. Find the totals of the frequency column (2^{nd} column) and the xf column (3^{rd} column).

The total of the frequency column is 13.

The total of the fx column is 149

Step 3. Finally, divide the total of the xf column by the total of the frequency column. This will give you the mean average.

149 ÷ 13 = 11.5 minutes rounded to the nearest tenth.

So the mean race time of 13 athletes was 11.5 minutes

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