Modal class

Here you will learn about modal class, including what it is and how to find the modal class from a grouped frequency table.

Students will first learn about modal class as part of statistics and probability in 6 th grade.

What is modal class?

In statistics, the modal class is the class interval within a set of data that has the highest frequency. This means it contains the most number of data points.

For example, below you have a set of data showing the grades achieved by 65 students in a test.

The class interval with the most number of data points is ‘71 to 80’ as this class interval has the highest frequency of 16 (the class interval contains 16 items of data).

You would therefore state:

The modal class is 71 to 80.

Modal class from a graph / chart

Given a bar chart, a pie chart, a stem-and-leaf plot, a frequency polygon, a cumulative frequency curve, or even a histogram, you can state the modal class. To do this, you will need to interpret the data from each graph.

Below is a table summarizing how to state the modal class from common types of graph / chart.

Type of chartThe modal class is…
Tally chart

… the class interval with the most
tally marks.

(Here, the modal class is ‘Green’).

Bar chart

… the class interval with the highest
bar.

(Here, the modal class is ‘Hockey’).

Pie chart

… the class interval with the largest
angle / area.

(Here, the modal class is ‘Apr-Jun’).

Histogram

… the class interval with the tallest bar.

(Here, the modal class is
1.5 m < x < 2m).

Common Core State Standards

How does this relate to 6 th grade math?

• Grade 6: Statistics and Probability (6.SP.B.5c)
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

How to find the modal class

In order to find the modal class:

1. Look for the class interval with the highest frequency.
2. Write down the modal class.

Modal class examples

Example 1: modal class from a frequency table

The grouped frequency table shows the number of people in 80 shops in a town.

State the modal class from the following table:

1. Look for the class interval with the highest frequency.

The highest frequency is 26.

2Write down the modal class.

The class with the highest frequency is ‘18 to 21’.

The modal class is ‘18 to 21’.

Example 2: modal class from a frequency table

The grouped frequency table shows the number of students in 90 elementary schools in an area.

State the modal class from the following set of data:

Look for the class interval with the highest frequency.

Write down the modal class.

Example 3: modal class from a frequency table

The grouped frequency table shows the grades achieved by 100 students in their science test.

State the modal class from the results table below:

Look for the class interval with the highest frequency.

Write down the modal class.

How to find the modal class from a graph / chart

In order to find the modal class from a graph / chart, you need to:

1. Look for the specific feature for the mode on the graph / chart.
2. Write down the modal class.

Modal class from a graph or chart examples

Example 4: modal class from a bar chart

The bar chart below shows the frequencies of pet ownership from a group of people. Each person owns one pet. State the modal class from the given data in the bar chart below.

Look for the specific feature for the mode on the graph / chart.

Write down the modal class.

Example 5: modal class from a pie chart

The points a basketball team scored in a season are recorded in a pie chart. Using the information below, determine the modal class for the set of data.

Look for the specific feature for the mode on the graph / chart.

Write down the modal class.

Example 6: modal class from a histogram

The histogram below represents the distance a ball was thrown by 40 people. State the frequency of the modal class.

Look for the class interval with the highest frequency.

Write down the modal class.

Teaching tips for modal class

• Before diving into finding the modal class, make sure students have a firm grasp on the basics of statistics, including what raw data is, how to create and read frequency tables, and what class intervals are.

• Provide step-by-step instructions to students on how to find the modal class. This includes displaying the information within the classroom for students to refer back to when needed.

• For students who need to hear information more than once, recording a tutorial for them to refer back to when needed, or provide the recording to math tutors who can help reinforce the learning.

Easy mistakes to make

• Thinking there can only be one mode of grouped data
A data set can have no modes, one mode, or more than one mode. A data set with no modes means you will not use the mode as a measure of central tendency.

• Mode is not the same as frequency
Students may get confused between mode and frequency. It’s important to reinforce that the mode will be actual data points – NOT the frequency.

• Using the wrong class intervals notation
The class intervals used in grouped frequency tables can be written in different ways. Take care when writing them.
For example,
0 to 5
0 - 5
0\le x <5

• Confusing the modal class with finding the frequency that occurs most often
A number may appear more than once in a frequency column. This does NOT affect the modal class. The modal class is always indicated by the largest frequency, not the frequency that occurs the most often.
For example,

The modal class is ‘20 to 29’ as this interval has the highest frequency. (You do not need to consider the fact that the frequency ‘5’ appears twice in the frequency column.)

Practice modal class questions

1. The table shows the grouped data about the scores in 35 netball matches. State the modal class interval.

13

12

20 to 29

10 to 19

The highest frequency is 13. The associated class is ‘10 to 19’. So the modal class is ‘10 to 19’.

2. The table shows the grouped data about the number of eggs laid by 50 chickens in two weeks.  State the modal class interval.

18

12-14

6-8

9-11

The highest frequency is 18. The associated item is ‘6-8’. So the modal class is ‘6-8’.

3. The table shows the grouped data about the height of 100 trees in a forest. State the modal class interval.

15<h \leq 20

31

20<h \leq 25

24

The highest frequency is 31. The associated item is ‘15<h \leq 20’. So the modal class is ‘15<h \leq 20’.

4. The pie chart below shows the number of different types of candy in a jar. State the modal class for the pie chart.

Chocolate Discs

Gum Balls

Lollipops and Marshmallows

Lollipops

The largest segment of the circle is orange, which represents gum balls. (Angle 120^{\circ} ).

5. Data was recorded for the days of snowfall over winter in the town of Courtship from November to March. State the modal class.

December

February

January

November

The modal class has the highest frequency on the given bar chart.

The modal class is January because it has the highest bar.

6. The histogram below represents the data collected for a recent score on a road safety test.

Determine the modal class of the data.

10 \leq x<20

25 \leq x<30

30 \leq x<40

20 \leq x<25

The modal class has the largest area. The area of each class is:

The class interval with the largest area / highest frequency is 10 \leq x<20.

Modal class FAQs

What is the standard deviation?

The standard deviation is a value that summarizes the variation around the mean. It is another measure that can be calculated from the data in frequency tables.

What is a frequency distribution table?

A frequency distribution table is a chart that summarizes values and the frequency of each of the values.

What are the measures of central tendency?

The measures of central tendency are often known as the mean, median and mode. These measures will help you find the middle, or average, of a given data set.

What is the class interval?

The class interval refers to the size of each class in which a range of a variable is divided. When finding the modal class, the smallest number in a class interval is known as the lower limit of the modal class, and the largest number is known as the higher limit of the modal class.

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