The range is largest value - smallest value, and it is a single number, not an interval. It is the quickest measure of spread to calculate, which is why examiners like it for one-mark questions. Its weakness is that it depends entirely on the two most extreme values and ignores everything in between, so a single unusual reading can make a tightly clustered data set look wildly spread out. When that risk exists, the interquartile range is the better measure.
Calculating a range is genuinely a one-line job. The marks that get lost are elsewhere: writing the answer as an interval instead of a number, and failing to explain why the range is or is not appropriate when a comparison question asks for it.
Examiners rarely ask for the range on its own. They ask for it alongside an average, then ask which data set is more consistent, and that second part is where the reasoning marks live.
Range
largest value - smallest value
Answer form
one number, with a unit
Strength
fast, uses the actual extremes
Weakness
one outlier distorts it completely
Alternative
interquartile range, IQR = UQ - LQ
Interpretation
smaller range means more consistent
Note the last row carefully, because it is the one that carries marks in comparison questions. A smaller range means the data is more tightly grouped, which in context usually means more consistent, more reliable or more predictable.
Eight students scored the following marks out of 50: 31, 44, 27, 38, 41, 35, 29, 46. Find the range.
Solution
46.27.= 46 - 27 = 19.The step students get wrong
Writing the answer as "27 to 46". That describes the data but it is not the range. The range is the single value 19. Marks are lost every year on this alone, because the question says "find the range" and expects one number.
Two machines fill bottles. Their fill volumes in millilitres over seven trials are recorded. Machine A: 498, 501, 499, 500, 502, 499, 501. Machine B: 499, 500, 501, 500, 499, 501, 470. Compare the two machines using the range, and comment.
Solution
502, smallest 498, so range = 4 ml.501, smallest 470, so range = 31 ml.470 is responsible for the entire difference.The exam phrase to use: when a single value distorts the range, say that the range "is affected by extreme values" and that the interquartile range "is not, because it uses only the middle 50% of the data". That sentence is worth a mark on its own in comparison questions.
The interquartile range throws away the bottom quarter and the top quarter of the data and measures the spread of what remains, which is why an unusual reading at either end cannot touch it. Finding the quartiles it needs is covered in cumulative frequency curves and box plots.
On a box-and-whisker plot the range is the distance from the far left whisker tip to the far right whisker tip, because the whiskers reach the minimum and maximum. The box itself spans the interquartile range. Being able to point at both on the same diagram is a common exam question, and the visual makes the difference between the two measures obvious at a glance.
Is the range a single number or an interval?
A single number. Subtract the smallest value from the largest and state the result with its unit. Writing "from 27 to 46" describes the data but does not answer a question asking for the range.
Can the range be zero?
Yes. If every value in the data set is identical, the largest and smallest are the same and the range is zero. That means there is no spread at all, which is a perfectly valid answer.
Can the range be negative?
No. If you get a negative answer you have subtracted the wrong way round. Always take the largest minus the smallest, and check your answer is positive before writing it down.
When should I use the range rather than the interquartile range?
Use the range when the data has no extreme values and you want a quick measure that reflects the full spread. Switch to the interquartile range whenever one or two readings sit far away from the rest, since those would dominate the range.
How does this connect to the rest of E-Maths?
Range is one of three measures of spread you need, alongside the interquartile range and standard deviation. Comparison questions almost always pair a measure of spread with an average, which is why it appears with comparing two data sets.
— Mr Gan Math Tuition
Mr. Gan works through the comparison questions where choosing the right measure is the mark.
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