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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?

The modal class is the class interval within a set of data that contains the most number of data points, which you can view as the highest frequency.

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 1 US

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
Modal class table image 1

… the class interval with the most
tally marks.

(Here, the modal class is ‘Green’).




Bar chart
Modal class table image 2

… the class interval with the highest
bar.

(Here, the modal class is ‘Hockey’).




Pie chart
Modal class table image 3

… the class interval with the largest
angle / area.

(Here, the modal class is ‘Apr-Jun’).




Histogram
Modal class table image 4

… the class interval with the tallest bar.

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


What is modal class?

What is modal class?

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.

[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

Use this quiz to check your 2nd and 6th grade students’ understanding of frequency tables. 10+ questions with answers covering a range of 2nd and 6th grade frequency table topics to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

[FREE] Frequency Table Check for Understanding (Grade 2 and 6)

Use this quiz to check your 2nd and 6th grade students’ understanding of frequency tables. 10+ questions with answers covering a range of 2nd and 6th grade frequency table topics to identify areas of strength and support!

DOWNLOAD FREE

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:

Modal class 3 US

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

The highest frequency is 26.

Modal class 4 US

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:

Modal class 5 US

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:

Modal class 7 US

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.

Modal class 9 US

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.

Modal class 10 US

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.

Modal class 11 US

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,

    Modal class 13 US
    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.

 

Modal class 14 US

13

GCSE Quiz False

12

GCSE Quiz False

20 to 29

GCSE Quiz False

10 to 19

GCSE Quiz True

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.

 

Modal class 15 US

18
GCSE Quiz False

12-14
GCSE Quiz False

6-8
GCSE Quiz True

9-11
GCSE Quiz False

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.

 

Modal class 16 US

15<h \leq 20
GCSE Quiz True

31
GCSE Quiz False

20<h \leq 25
GCSE Quiz False

24
GCSE Quiz False

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.

 

Modal class 17 US

Chocolate Discs

GCSE Quiz False

Gum Balls

GCSE Quiz True

Lollipops and Marshmallows

GCSE Quiz False

Lollipops

GCSE Quiz False

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.

 

Modal class 18 US

December

GCSE Quiz False

February

GCSE Quiz False

January

GCSE Quiz True

November

GCSE Quiz False

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.

 

Modal class 19 US

 

Determine the modal class of the data.

10 \leq x<20
GCSE Quiz True

25 \leq x<30
GCSE Quiz False

30 \leq x<40
GCSE Quiz False

20 \leq x<25
GCSE Quiz False

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

 

Modal class 20 US

 

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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