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Academy11+

11+ Maths · Topic explained

Median, mode and range

Which number is in the middle, which is the most common, and how spread out are they?

The big idea

Median = the middle in order. Mode = the most common. Range = biggest − smallest.

Picture it

Line a team up by height: the one in the middle is the median.

Key words

median
The middle value once they're in order.
mode
The value that appears most often.
range
Biggest take away smallest: how spread out the values are.

Worked examples

  1. 1Warm-up

    Find the median of 7, 2, 9, 4, 5.

    • In order: 2, 4, 5, 7, 9
    • The middle one is 5
  2. 211+ standard

    Find the median of 8, 3, 10, 6.

    • In order: 3, 6, 8, 10
    • Two middle numbers: halfway between 6 and 8
    • Median = 7
  3. 311+ standard

    Find the mode and the range of 4, 7, 4, 9, 2, 4, 7.

    • 4 appears three times: mode = 4
    • Range = 9 − 2 = 7
  4. 411+ standard

    Midnight temperatures: −3 °C, 4 °C, 1 °C, −1 °C. Find the range.

    • Highest 4, lowest −3
    • 4 − (−3) = 4 + 3 = 7 degrees

The common mistake

The mistake

The median of 7, 2, 9 is 2, because 2 is in the middle of the list.

Instead

Put them in order first: 2, 7, 9, so the median is 7.

Why: The median is the middle of the values in order, not the middle of the list as written.

Where it comes up in the 11+

Find all three from a list or a chart, or a missing value that gives a certain median or range.

The video

Video coming soon

We're making a short video that explains median, mode and range step by step. Until then, everything it covers is on this page.

Free printable

Median, mode and range worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. What is the median of 3, 9, 1, 7, 5?

    • 1
    • 5
    • 7
    • 9
    Show the answer

    5

    In order: 1, 3, 5, 7, 9. The middle one is 5.

  2. 2. What is the mode of 6, 2, 6, 8, 2, 6?

    • 2
    • 6
    • 8
    • 5
    Show the answer

    6

    6 appears three times, more than any other number.

  3. 3. What is the range of 12, 5, 20, 9?

    • 15
    • 8
    • 11.5
    • 20
    Show the answer

    15

    Biggest 20 − smallest 5 = 15.