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Modal Class and Median Class

FoundationHigherAQAEdexcel

Practise Modal Class and Median Class for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. For grouped data we identify the modal class and the class containing the median rather than single values.

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

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

With grouped data the mode and median cannot be found exactly, so the modal class and the median class are identified instead.

The modal class is the class interval with the highest frequency. When class widths are unequal, the class with the highest frequency density is the modal class, since a wide class may have a high frequency simply because it covers more values.

The median class is the class containing the middle value. Find the position using \(\frac{n}{2}\) for grouped data, then use a running total of the frequencies to identify which class that position falls in. The answer to both is an interval, not a single number.

Revision notes

The modal class

The class interval with the highest frequency.

When class widths are unequal, use the highest frequency density instead, because a wide class may have a high frequency simply because it spans more values.

The median class

Find the position of the middle value using \(\frac{n}{2}\), where \(n\) is the total frequency.

Work through a running total of the frequencies until that position is reached or passed. The class you are in at that point is the median class.

Giving the answer

Both answers are intervals, not single numbers.

Writing a single value loses the mark. Write the full class such as \(20 \leq x < 30\), exactly as it appears in the table.

Key points

  • The modal class has the highest frequency.
  • Use frequency density if class widths are unequal.
  • The median class contains the middle value.
  • Find the position using n ÷ 2.
  • Use a running total to locate the class.
  • Both answers are intervals, not single values.

Worked examples

Example 1

Classes have frequencies 7, 15, 9 and 4. State the modal class frequency. [1 mark]

Working

15identify the highest frequency

Example 2

A grouped table has total frequency 60. Work out the position used to find the median class. [2 marks]

Working

\(\frac{60}{2}\)halve the total frequency
\(= 30\), so find the class containing the 30th valuestate the position

Example 3

Explain why the modal class is used rather than the mode for grouped data. [2 marks]

Working

The individual values are lost when data is groupedstate what is lost
so the single most common value cannot be identified, only the class containing the most valuesexplain the consequence

Common mistakes

  • Giving a single value as the modal class.

    The answer must be the full interval.

  • Using frequency when class widths are unequal.

    Use frequency density instead.

  • Confusing the modal class with its frequency.

    The modal class is the interval, not the frequency it contains.

  • Forgetting the running total for the median class.

    It is needed to locate which class contains the middle value.

Exam tips

  • Write the full interval as your answer.
  • Check whether class widths are equal first.
  • Use a running total to find the median class.
  • Use n ÷ 2 for grouped data.

Key terms

Modal class
The class interval with the highest frequency.
Median class
The class interval containing the middle value.
Frequency density
Frequency divided by class width.
Running total
A cumulative sum of frequencies.

Related topics

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