Often we may want to calculate the mode of data that is grouped in some way.

Recall that the mode represents the value that occurs most frequently.

For example, suppose we have the following grouped data:

While it’s not possible to calculate the exact mode since we don’t know the raw data values, it is possible to estimate the mode using the following formula:

**Mode of Grouped Data = L + W[(F _{m} – F_{1})/( (F_{m}-F_{1}) + (F_{m} – F_{2}) )]**

where:

**L**: Lower limit of modal class**W**: Width of modal class**F**: Frequency of modal class_{m}**F**: Frequency of class immediately before modal class_{1}**F**: Frequency of class immediately after modal class_{2}

**Note**: The **modal class** is simply the class with the highest frequency. In the example above, the modal class would be 21-30 since it has the highest frequency.

The following examples show how to calculate the mode of grouped data in different scenarios.

**Example 1: Calculate the Mode of Grouped Data**

Suppose we have the following frequency distribution that shows the exam scored receive by 40 students in a certain class:

In this example, the **modal class** is 71-80.

Knowing this, we can calculate the following values:

**L**: Lower limit of modal class:**71****W**: Width of modal class:**9****F**: Frequency of modal class:_{m}**15****F**: Frequency of class immediately before modal class:_{1}**8****F**: Frequency of class immediately after modal class:_{2}**8**

We can plug these values into the formula to calculate the mode of the distribution:

- Mode = L + W[(F
_{m}– F_{1})/( (F_{m}-F_{1}) + (F_{m}– F_{2}) )] - Mode = 71 + 9[(15-8) / ( (15-8) + (15-8) )]
- Mode =
**75.5**

We estimate that the modal exam score is **75.5**.

**Example 2: Calculate the Mode of Grouped Data**

Suppose we have the following frequency distribution that shows the number of points scored per game by 60 basketball players:

In this example, the **modal class** is 11-20.

Knowing this, we can calculate the following values:

**L**: Lower limit of modal class:**11****W**: Width of modal class:**9****F**: Frequency of modal class:_{m}**25****F**: Frequency of class immediately before modal class:_{1}**8****F**: Frequency of class immediately after modal class:_{2}**14**

We can plug these values into the formula to calculate the mode of the distribution:

- Mode = L + W[(F
_{m}– F_{1})/( (F_{m}-F_{1}) + (F_{m}– F_{2}) )] - Mode = 11 + 9[(25-8) / ( (25-8) + (25-14) )]
- Mode =
**16.46**

We estimate that the modal points scored is **16.46**.

**Additional Resources**

The following tutorials explain how to perform other common operations with grouped data:

How to Find Mean & Standard Deviation of Grouped Data

How to Find the Median of Grouped Data

How to Calculate Percentile Rank for Grouped Data

In my class the teacher always ignores the h, which is here defined as the width of the modal class. Is it ok to ignore it you’re using a different formula here?

What happens if the modal class is the first or the last class? Do we just plug in a 0 in the formula?

It is really helpful I didn’t think so but the graphics need some improvement

Good.

I want to join you in your email.