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Mode from a Frequency Table

FoundationChallengeAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on mode from a frequency table helps you revise finding the mode from a frequency table. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. The mode is the value with the highest frequency.

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Topic overview

A frequency table groups data by value, showing how many times each one occurs. Finding the mode from such a table is the most direct of the three averages.

The mode is the value with the highest frequency, not the highest frequency itself. If the score \(3\) occurs \(11\) times and that is the largest frequency, the mode is \(3\), not \(11\).

That distinction is the single most common error in the topic. The frequency column tells you how often something happened; the value column tells you what happened, and the mode is a value.

Revision notes

Reading the table

One column lists the values and the other lists how often each occurs.

For scores \(1\) to \(5\) with frequencies \(4, 7, 11, 6, 2\), the largest frequency is \(11\), which belongs to the score \(3\).

The mode is a value

Find the largest frequency, then read across to the value beside it.

In the example above the mode is \(3\). Giving \(11\) as the answer confuses the count with the thing being counted.

More than one mode

If two values share the highest frequency, both are modes and the data is bimodal.

If no value occurs more often than the others, there is no mode at all.

Key points

  • A frequency table shows how often each value occurs.
  • The mode is the value with the highest frequency.
  • The mode is not the frequency itself.
  • Read across from the largest frequency to its value.
  • Two values can share the mode, making the data bimodal.
  • Data with all frequencies equal has no mode.

Worked examples

Example 1

Scores \(1, 2, 3, 4\) have frequencies \(5, 9, 3, 2\). Find the mode.

Working

\[\text{Largest frequency is } 9\]find the highest frequency
\[\text{It belongs to score } 2\]read across to the value
\[\text{Mode} = 2\]state the mode

Example 2

Values \(10, 20, 30\) have frequencies \(7, 7, 4\). Find the mode.

Working

\[\text{Two values share the highest frequency}\]10 and 20 both occur 7 times
\[\text{Modes are } 10 \text{ and } 20\]the data is bimodal

Example 3

Explain why the mode of a frequency table is never the frequency.

Working

\[\text{The frequency counts occurrences}\]it tells you how often
\[\text{The mode is the value that occurred}\]it tells you what

Common mistakes

  • Giving the frequency as the mode.

    The mode is the value beside the largest frequency, not the frequency itself.

  • Assuming there is always exactly one mode.

    Two values can tie, and sometimes there is no mode at all.

  • Choosing the largest value rather than the most frequent.

    Look down the frequency column, not the value column.

  • Confusing the mode with the median.

    The mode is the most common value; the median is the middle one.

Exam tips

  • Look down the frequency column for the largest number.
  • Read across to the value beside it.
  • Check whether two values tie for the highest frequency.
  • State clearly which column your answer comes from.

Key terms

Frequency table
A table showing how often each value occurs.
Mode
The most frequently occurring value.
Bimodal
Having two modes.
Frequency
The number of times a value occurs.

Related topics

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