Skip to content
VirtusAcademy

Modal Class from a Frequency Table

FoundationHigherAQAEdexcelOCR

Master modal class from a frequency table for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers finding the modal class and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. The modal class is the group with the highest frequency.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

The modal class is the class with the highest frequency in a grouped frequency table. It is the grouped-data equivalent of the mode.

Because the individual values are unknown, you cannot identify a single modal value — only the class it falls in. So the answer is a range such as \(20 \le x < 30\), not a single number.

This assumes the classes are of equal width. If they are not, the class with the highest frequency may not be the most densely populated, and frequency density would be needed instead.

Revision notes

Finding the modal class

Look down the frequency column for the largest value, then give the class beside it.

With frequencies \(6, 14, 9, 3\) for four classes, the modal class is the second one.

Giving the answer as a range

The answer is a class, written as an inequality such as \(20 \le x < 30\).

Giving a single number is wrong, because grouping means the exact values are unknown.

Unequal class widths

If the classes have different widths, compare frequency density rather than raw frequency.

Frequency density is frequency divided by class width, and it corrects for the fact that a wider class naturally collects more values.

Key points

  • The modal class has the highest frequency.
  • The answer is a class, not a single value.
  • Write it as an inequality such as \(20 \le x < 30\).
  • Individual values are unknown in grouped data.
  • Use frequency density if class widths differ.
  • Frequency density is frequency divided by class width.

Worked examples

Example 1

Classes \(0-10\), \(10-20\), \(20-30\) have frequencies \(8, 15, 6\). Find the modal class.

Working

\[\text{Largest frequency is } 15\]find the highest frequency
\[10 \le x < 20\]give the class beside it

Example 2

Why is the answer a class rather than a single value?

Working

\[\text{Grouped data hides individual values}\]the exact figures are unknown
\[\text{So only the class can be identified}\]state the reason

Example 3

A class of width \(20\) has frequency \(30\). Find its frequency density.

Working

\[30 \div 20\]divide frequency by class width
\[= 1.5\]state the frequency density

Common mistakes

  • Giving a single value as the modal class.

    The answer must be the class, written as a range.

  • Giving the frequency instead of the class.

    The modal class is the range, not how many values it contains.

  • Ignoring unequal class widths.

    With different widths, compare frequency density rather than frequency.

  • Confusing modal class with median class.

    The modal class has the highest frequency; the median class contains the middle value.

Exam tips

  • Look down the frequency column for the largest value.
  • Write the answer as the class inequality.
  • Check whether the class widths are equal.
  • Use frequency density when they are not.

Key terms

Modal class
The class with the highest frequency.
Grouped frequency table
A table sorting data into classes.
Frequency density
Frequency divided by class width.
Class width
The size of the interval covered by a class.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.