# 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

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

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

**Question:** What is the modal class if frequency numbers are 2,5,7,3,6,2,0,1?

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

**Question:** What is the modal class if the frequency numbers are 0,4,2,7,8,1?

**Answer:** It will be the group containing the highest frequency, so since 8 is the highest frequency then it will be this group.

**Question:** What is the modal score for 25,15,30,40,10?

**Answer:** 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.

**Question:** What is the modal class interval if the frequency numbers are 3, 6, 10, 12, 9?

**Answer:** It will be the group containing the highest frequency.

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

**Question:** How do you solve for the mode of the grouped data in example 2?

**Answer:** The mode is the group which has the highest frequency in it.

In example 2 there are two groups which contain the highest frequency, so is bimodal.

**Question:** How to find mode on grouped data with 2 modal classes?

**Answer:** The answer will be both these groups, it will be bimodal.

**Question:** What is the modal class if the frequencies are 14,9,11,2,14?

**Answer:** There will be two group for the modal class (Bimodal).

These will be the groups corresponding to the 14.

**Question:** What is the modal class if the frequency numbers are 3,2,7,8,0?

**Answer:** The modal class is the group with the highest frequency.

So it will be the group matching the 8.

**Question:** What is the modal class if the frequency numbers are 18, 20, 22 , 24 ,26?

**Answer:** The modal group is the group containing the largest frequency which is the group corresponding to 26.

**Question:** What is the modal class if frequency numbers are 7,13,15,6,17,12?

**Answer:** The modal class is the group with the highest frequency.

So it will be the group corresponding to 17.

**Question:** What is the modal class if the frequency number is 2, 1, 4, 3?

**Answer:** The modal class is the group containing the highest frequency.

Since 4 is the highest number it will be the grup matching this.

**Question:** What is the mode if the frequency: 20,12,15,14,11,9,13, and 6?

**Answer:** The mode will be the group with the highest frequency.

20 is the highest frequency in this list, so it will be the group corresponding to the 20.

**Question:** How should we deal with a question that involves two modal class intervals?

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

**Question:** What is the modal class if the frequency numbers are 7,3,3,5,3,7,2? Kindly explain how to compute for the mean.

**Answer:** The modal class is the group with the highest frequency.

In this case, it is the two groups corresponding to 7.

To work out the mean you will need to multiply the midpoint of each group by the frequency, add this column up, and divide the answer by the total frequency.

**Question:** What is the modal weight if the frequency numbers are 3,6,5,1?

**Answer:** It will the weight which matches with the 6, as 6 is the highest frequency number.

**Question:** What if the modal class is the first or the last one?

**Answer:** Neither of them, the modal is the group which has the highest frequency number.

**Question:** What is the modal class if frequency numbers are 1, 3, 8, 11, 11, 9, 5 and 2?

**Answer:** There will be two modes (bi modal).

The two groups corresponding to the 11's.

**Question:** 6,30,40,16,4,4. Find the mode?

**Answer:** The mode is the group matching 40.

**Question:** What is the modal class if the frequency numbers are 5, 8, 12, 13, 11?

**Answer:** The group corresponding to 13.

**Question:** If the least mark obtained in the history test is 18%, and the range of the marks was 70%. What was highest mark scored in the history test?

**Answer:** Just add 70 % and 18% to give 88%.

**Question:** What is the modal class interval if the frequency numbers are 2,8,9,7,4?

**Answer:** The modal group is the one which has the highest frequency associated with it.

So since 9 is the highest number, then it will be the group matching the 9.

**Question:** How to solve mode in the frequency table?

**Answer:** Look for the highest frequency in the table, and the group or value corresponding to this will be the mode.

**Question:** What is the modal class if the frequency numbers are 12,10,16,20,18,14,6,4 ?

**Answer:** 20 is the largest number, so the group corresponding to the 20 in the frequency table will be the modal class.

## Comments

**Evidence Kudzotsa** on April 17, 2019:

why is it that the upper class limit of the first class is also the lower class limit of the next class. According to the example given, the classes are like this 40-50, 50-55, 55-60, lets say for instance someone weighs 50kgs, will that person be in the class of 40-50 or in the class of 50-55? I initially thought that classes should be like this 30-39,40-49,50-59 etc, this helps to avoid members to belong to more than 1 class. Please kindly assist.