The four everyday statistics, and every twist an exam adds — odd and even data sets, the median between two middle values, finding a missing value from the mean, and working back from a total — each worked in full, with a worksheet.
Data handling asks you to summarise a set of numbers. Four values do most of the work: the mean, median and mode (three kinds of average) and the range (a measure of spread). This guide covers each — plus the harder exam twists learners often miss.
- Mean — add all the values, divide by how many there are.
- Median — the middle value once the data is in order.
- Mode — the value that appears most often (there can be more than one, or none).
- Range — the largest value minus the smallest.
1Type 1: All four from one data set (odd number of values)
- 1Mean: (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8.Add all five, divide by 5.
- 2Median: put in order (already ordered), the middle (3rd) value is 7.5 values → the 3rd is the middle.
- 3Mode: 7 (appears twice).Most frequent value.
- 4Range: 13 − 4 = 9.Highest minus lowest.
2Type 2: Median of an EVEN number of values
With an even count there is no single middle — the median is the average of the two middle values.
- 1Order the data: 3, 5, 8, 10 (already ordered).Always order first.
- 2The two middle values are 5 and 8.4 values → positions 2 and 3 are the middle.
- 3Median = (5 + 8) ÷ 2 = 6,5.Average the middle two.
3Type 3: Finding a missing value from the mean
Work backwards: if you know the mean and how many values there are, the total = mean × count.
- 1Total needed = mean × count = 7 × 4 = 28.Sum = mean × number of values.
- 2Known values add to 6 + 9 + 5 = 20.Add the ones you have.
- 3x = 28 − 20 = 3.The missing value makes the total reach 28.
4Type 4: Which average is fairest? (outliers)
- 1Mean = (8+9+10+11+60) ÷ 5 = 98 ÷ 5 = 19,6.The single value 60 drags the mean up.
- 2Median = 10 (the middle value).The median ignores how extreme the outlier is.
- 3Here the median (10) describes 'typical' better than the mean (19,6).One outlier distorts the mean, not the median.
Always put the data in order before finding the median or range. For an even number of values, the median is the average of the middle two — this is the most commonly missed case.
The mean can be pulled by outliers. One very large or small value shifts the mean but not the median — which is why the median is often the fairer 'average' for skewed data.
These statistics run through Grade 8–12 and all of Maths Literacy. Work through every type in the worksheet below.
Practice exercises
Work each one out, then click to reveal the answer.
- 1Find the mean of 3, 5, 10, 2 (mean)
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20 ÷ 4 = 5 - 2Find the mean of 12, 15, 18, 15 (mean)
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60 ÷ 4 = 15 - 3Find the median of 8, 3, 9, 5, 6 (median, odd)
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Order 3,5,6,8,9 → 6 - 4Find the median of 4, 10, 6, 8 (median, even)
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Order 4,6,8,10 → (6+8)÷2 = 7 - 5Find the mode of 2, 4, 4, 4, 7, 9 (mode)
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4 (appears three times) - 6Find the range of 15, 22, 9, 30 (range)
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30 − 9 = 21 - 7The mean of 4, 8, x, 6 is 7. Find x. (missing value)
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Total 7×4 = 28; 28 − 18 = 10 - 8The mean of 5 numbers is 12. What is their total? (work back)
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12 × 5 = 60 - 9Data: 6, 6, 7, 8, 40. Which is more typical, mean or median? (outlier)
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Mean 13,4 vs median 7 → median (40 is an outlier) - 10Find all four (mean, median, mode, range) for 2, 3, 3, 6 (all four)
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Mean 14÷4 = 3,5; median (3+3)÷2 = 3; mode 3; range 6−2 = 4
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