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Statistics & Probability ยท Foundation & Higher

Mean, median, mode & range

Averages summarise a data set with a single representative value. The range measures spread.

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Key facts to remember

  • 1Mean = sum of all values รท number of values.
  • 2Median = middle value when data is ordered (or mean of middle two for even-sized data).
  • 3Mode = most frequently occurring value (there can be more than one).
  • 4Range = largest value โˆ’ smallest value.
  • 5The mean is affected by outliers; the median is not.
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Formulas

Mean
xฬ„ = ฮฃx / n

ฮฃx = sum of all values, n = count

Range
Range = Max โˆ’ Min
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Worked examples

Example 1

Find the mean, median, mode and range of: 3, 7, 7, 2, 9, 4, 7

Working

  1. Order: 2, 3, 4, 7, 7, 7, 9
  2. Mean = (2+3+4+7+7+7+9) รท 7 = 39 รท 7 = 5.57 (2 d.p.)
  3. Median = 4th value = 7
  4. Mode = 7 (appears 3 times)
  5. Range = 9 โˆ’ 2 = 7
AnswerMean โ‰ˆ 5.57, Median = 7, Mode = 7, Range = 7
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Common mistakes

โœ—Forgetting to sort the data before finding the median.
โœ—Finding the median position incorrectly for even-sized data (should average the two middle values).
โœ—Confusing mode (most common) with mean (average).
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Exam tips

โœ“Always sort the data first โ€” write the ordered list out clearly.
โœ“For n data points, the median is at position (n+1)/2.

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