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Mean, median, mode & range reference

Mean, median, mode and range reference

Print a reference that explains mean, median, mode and range with worked examples. Compare odd and even datasets, negative values, tied modes and data with no mode.

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Reference · LetterReference · A4
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Read each definition alongside its worked example. Put the observations in numerical order before finding the median, and count every repeated value before deciding the mode.

Download the complete reference with its explanations and worked examples. This handout does not need a separate answer key.

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Reference handout
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Paper sizes and printing help · More mean, median, mode & range activities

Keep the definitions beside the data

The English reference uses two pages to explain the four measures with worked examples. It includes even and odd dataset lengths, negative values, several modes and no mode. The examples and explanations are part of the handout; there is no separate answer key.

Print in US Letter or A4. Use the reference during a short practice set, then ask learners to explain the difference between the measures in their own words.

Learning objective

What this activity builds

Explain what each statistic describes and choose the correct calculation for a raw dataset.

Worked example

Find the mean, median, mode and range of 7, 3, 5, 5.

Mean = 5. Median = 5. Mode = 5. Range = 4.

The sum is 20, so the mean is 20 ÷ 4 = 5. In order, the values are 3, 5, 5, 7; the two middle values average to 5. The value 5 appears most often. The range is 7 − 3 = 4.

Teaching notes

Make the practice count

  • Describe mean as a fair-share value, median as a middle value and mode as the most frequent value.
  • Use one dataset to compare the four calculations before moving to several different sets.
  • Include an even-sized example so students practice averaging the two middle values.
  • Discuss a dataset with no repeated values and one with several equally frequent repeated values.

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2 reference pages
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Math SheetNameScoreTeacherDateMean, Median, Mode and Range ReferenceOrder the data before finding its center. Compute every answer from the observations shown.Ordering numbersSort from least to greatest. Negative numbers farther left on a number line are smaller.-8, -3, -3, 2, 7Arithmetic meanAdd every observation and divide by the number of observations.2, 4, 4, 6: 16 ÷ 4 = 4Odd medianAfter sorting an odd-sized dataset, choose its one central observation.-7, -2, 4, 6, 9: median 4Even medianAverage the two central observations. Their average may be negative or a half.-8, -6, -3, -3: median (-6 + -3) ÷ 2 = -4.5math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDateMean, Median, Mode and Range ReferenceOrder the data before finding its center. Compute every answer from the observations shown.One modeA mode is a repeated observation with the greatest frequency.2, 2, 5, 7: mode 2Several modesList every repeated observation tied for greatest frequency, in numerical order.1, 1, 3, 3, 6, 6, 9, 9, 12: modes 1, 3, 6, 9No modeIf every observation occurs once, there is no mode.-4, -1, 3, 8: no modeRangeSubtract the minimum from the maximum. Range is never negative.-9, -4, 2, 7: 7 - (-9) = 16math-sheet.comPage 2 / 2

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