# How to Work out the Modal Class Interval from a Grouped Frequency Table

## How To Work Out The Modal Class Interval From A Frequency Table Video

Finding the modal class from a grouped frequency table is actually quite easy to do. All you need to do is to look for the group that has the highest frequency. This is because the mode is the number that comes up the most times. Make sure you write the group down and not the frequency. If you do this you will not score any marks. In most exams finding the modal class will only be worth one mark as there is no working out to show. So just remember to look for the group with the highest frequency.

Let’s take a look at some examples that involve finding the modal class from a grouped frequency table.

**Example 1**

The frequency table shows the weights of some patients a doctors surgery. 13 people have a weight 60kg up to 70kg, 2 people have a weight 70kg up to 75kg, 45 people have a weight 75kg up to 95kg and 7 people have a weight 95 up to 100kg. Write down the modal class interval.

So all you need to do is look for the group that contains the highest frequency. There were 45 people who had a weight between 75kg and 95kg so this will be the modal group.

Therefore the modal class interval is 75kg up to 95kg.

**Example 2**

The frequency table shows the race times of a group of athletes who took part in a 400m race. 6 people completed the 400m race in a time 45 seconds up to 50 seconds, 9 people completed the race in a time 50 seconds up to 55 seconds, 9 people completed the race in a time 55 seconds up to 60 seconds and the remaining 3 athletes completed the race in a time of 60 up to 65 seconds. Work out the modal class interval for these race times.

Like the last example all you need to do is look at the frequency column and pick out the group that contains the highest frequency. However, in this example there are two groups with the same frequency – 9 people completed the race in a time 50 seconds up to 55 seconds and also 9 people completed the race in a time 55 up to 60 seconds. Therefore, there are two modal classes (known as bimodal).

Therefore the modal class intervals are 50 up to 55 and 55 up to 60.

So as you can see working out the modal class interval is very quick and easy to do. However, working out the mean and median can be harder to work out (see below for help on finding the mean and median from a frequency table).

## Questions & Answers

What is the modal class if the frequency numbers are 8, 19, 7, 4, 1?

You will be looking for the group with the highest frequency. So this will be the group corresponding to 19.

Helpful 140What is the modal class if frequency numbers are 2,5,7,3,6,2,0,1?

It will be the group containing the 7, as 7 is the highest frequency.

Helpful 73What is the modal class interval if the frequency numbers are 3, 6, 10, 12, 9?

It will be the group containing the highest frequency.

So the modal group will be the one that has 12 as the frequency.

Helpful 24How should we deal with a question that involves two modal class intervals?

You will write both groups down as the answer is bimodal.

Helpful 3What is the modal score for 25,15,30,40,10?

It will be the score with the highest frequency. So since 40 is the highest frequency, then it will be the group corresponding to this number.

Helpful 20

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