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Functional Skills Level 2 — Statistics

The Range

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Real-World Applications

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What Is the Range?

\[\text{Range} = \text{Maximum value} - \text{Minimum value}\]

The range is a measure of spread: subtract the smallest value in a dataset from the largest value. Range = highest value − lowest value. It is not an average — it only tells you how spread out the data is, not where the middle of it lies.

Range shown on a number line 0 2 4 6 8 10 12 14 3 5 7 9 12 MAX MIN=3 Range = 12 − 3 = 9 Range = SPREAD, not an average A large range = data spread out. A small range = data clustered together.

Example 1 — Range of 4, 9, 2, 7, 11, 5

Step 1
Maximum = 11, Minimum = 2
Step 2
Range = \(11 - 2 = \mathbf{9}\)

Example 2 — Test scores: 55, 62, 78, 45, 90, 68

Step 1
Max = 90, Min = 45
Step 2
Range = \(90 - 45 = \mathbf{45}\) marks
Step 3
A range of 45 marks shows the scores are quite spread out.
⚠ Common mistake: The range is not an average — never write "the range is 9 so the typical value is 9". The range only tells you how spread out the data is.

✓ Quick Check 1 — Calculating the range

Question 1 of 10

Using Range in Context — Comparing Consistency

A small range means the data is consistent (close together). A large range means the data is spread out (variable). The range is often used to compare two groups.

Comparing Two Teams by Range Team A Scores: 78, 80, 82, 79, 81 Max=82, Min=78 Range = 4 CONSISTENT Small range → reliable Team B Scores: 55, 90, 70, 40, 95 Max=95, Min=40 Range = 55 INCONSISTENT Large range → variable Dot Plots — Team A vs Team B 40 60 78–82 90 95 Team A Team B (spread)

Example 3 — Comparing two runners

Runner A: 10.2, 10.4, 10.1, 10.3, 10.5 seconds. Runner B: 9.8, 11.2, 10.0, 11.8, 9.9 seconds.

Step 1
Runner A range: \(10.5 - 10.1 = 0.4\text{s}\)
Step 2
Runner B range: \(11.8 - 9.8 = 2.0\text{s}\)
Step 3
Runner A has a smaller range — more consistent performance.

Example 4 — Mean and range together

Two groups both have a mean of 70, but Group X range = 5 and Group Y range = 40.

Step 1
Same mean → similar typical performance
Step 2
Group X: more consistent (range 5). Group Y: much more variable (range 40).
Step 3
Use both mean AND range to fully describe a dataset.
Exam tip: When comparing two groups, comment on BOTH the average (mean/median) and the spread (range).

✓ Quick Check 2 — Interpreting range in context

Question 1 of 10

Range with Negative Numbers

The formula is the same — Range = Max − Min. Be careful when the minimum is negative: subtracting a negative number means adding.

Temperature Range — Negative Minimum -10 -8 -5 0 5 10 15 MIN = -8°C MAX = 15°C Range = 15 − (−8) = 15 + 8 = 23°C Key rule: Max − (negative Min) = Max + |Min| 15 − (−8) = 15 + 8 = 23 | 3 − (−5) = 3 + 5 = 8

Example 5 — Weekly temperatures: −3, 5, −8, 10, 2, −1, 7°C

Step 1
Maximum = 10°C, Minimum = −8°C
Step 2
Range = \(10 - (-8) = 10 + 8 = \mathbf{18}°\text{C}\)

Example 6 — Golf scores (under par is negative): −4, −2, 0, 3, −1, 5

Step 1
Max = 5, Min = −4
Step 2
Range = \(5 - (-4) = 5 + 4 = \mathbf{9}\) strokes
Step 3
A range of 9 strokes shows inconsistent scoring.
⚠ Common mistake: Students write Range = Max − |Min| without flipping the sign. Remember: subtracting a negative is the same as adding its positive value.

✓ Quick Check 3 — Range with negatives and real-life context

Question 1 of 10

Try It: Range Summary

Key range calculations to verify your understanding.

#DataRange
14, 9, 2, 7, 119
2−3, 5, −8, 1018
3Team A: 78,80,82 (range?)4
4Team B: 55,90,40,95 (range?)55
56, 6, 6, 60

Practice: Finding the Range

Enter your answers as numbers.

#QuestionAnswerResult
1Find the range of 4, 9, 15, 3, 22
2Find the range of 55, 60, 48, 72, 65
3Find the range of 100, 100, 100, 100
4Find the range of −5, 3, 8, −2
5Find the range of 12.5, 9.2, 15.8, 7.1
6Find the range of 30, 45, 20, 60, 35
7Find the range of −8, 2, −3, 6
8Find the range of 200, 350, 275, 400
9Find the range of 1.5, 2.8, 0.9, 3.2
10Find the range of 7, 21, 14, 3, 28

⚠ Things to Watch Out For

  • Thinking range is an average: Range is a measure of SPREAD, not an average. It tells you how spread out the data is, not what a typical value is.
  • Subtracting maximum from minimum: Range = MAXIMUM − MINIMUM (not the other way round). The range is always positive.
  • Including outliers: The range is heavily influenced by outliers. One very large or very small value dramatically increases the range — this may not represent the typical spread.
  • Range with negative numbers: Range of {−5, −2, 3, 7} = 7 − (−5) = 12 (subtract a negative = add). Don't write 7 − 5 = 2.
  • Range tells you nothing about distribution: Two data sets can have the same range but very different distributions. Range alone doesn't describe how spread out the data is within that range.
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