Statistics
Grade 2-4Range & Spread
The range measures how spread out a set of data is, and comparing ranges is one of the most common ways GCSE Maths tests whether one data set is more consistent than another. This lesson covers finding the range of a list and from a frequency table, finding a missing value when the range is known, and using the range alongside the mean to compare consistency.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Finding the range of a list
The range is the difference between the largest and smallest values in a set of data, found by subtracting the smallest from the largest.
For the list 3, 7, 5, 12, 2, 9, the largest value is 12 and the smallest is 2, so the range is 12 − 2 = 10.
Finding the range from a frequency table
Find the largest and smallest data values that actually have a frequency of at least 1, ignoring any values with a frequency of 0, then subtract as usual.
A table shows the number of siblings for 20 students, with frequencies given for 0 to 4 siblings. If every value from 0 to 4 has a frequency of at least 1, the largest value with a frequency is 4 and the smallest is 0, so the range is 4 − 0 = 4.
Finding a missing value from a known range
If the range and all but one value are known, decide whether the missing value is the highest or the lowest, then add or subtract the range from the known extreme value accordingly.
The range of the heights of 5 plants is 24 cm. Four heights are 18, 30, 22, 15, and the fifth plant is the tallest. The smallest known height is 15, so the tallest height is 15 + 24 = 39 cm.
Using the range to compare consistency
A smaller range means the data is more consistent, since the values are closer together. When comparing two data sets, find the range for each one, then state that the set with the smaller range is more consistent. If a question also asks for the mean, find both the mean and range for each set, since equal means combined with different ranges still shows a clear difference in consistency.
Machine A's output weights have a range of 102 − 98 = 4, and Machine B's have a range of 110 − 90 = 20. Since 4 is smaller than 20, Machine A is more consistent.
Worked Examples
Three exam-style questions, fully solved.
Find the range of this list of numbers: 3, 7, 5, 12, 2, 9.
Easy- 1.Identify the largest and smallest values: largest = 12, smallest = 2
- 2.Subtract the smallest from the largest: 12 − 2
Answer: 10
The range of the heights of 5 plants (in cm) is 24. Four of the heights are 18, 30, 22, 15. The fifth plant is the tallest. Find its height.
Medium- 1.Identify the smallest known height: 15 cm
- 2.Add the range to the smallest height, since the missing plant is the tallest: 15 + 24
Answer: 39 cm
Two athletes' long jump distances (m) in 5 attempts: Athlete A: 5.2, 5.5, 5.1, 5.4, 5.3. Athlete B: 4.8, 5.9, 4.5, 6.0, 5.3. Find the mean and range for each athlete, then state which athlete is more consistent.
Hard- 1.Find the mean and range for Athlete A: mean = (5.2 + 5.5 + 5.1 + 5.4 + 5.3) ÷ 5 = 5.3 m, range = 5.5 − 5.1 = 0.4 m
- 2.Find the mean and range for Athlete B: mean = (4.8 + 5.9 + 4.5 + 6.0 + 5.3) ÷ 5 = 5.3 m, range = 6.0 − 4.5 = 1.5 m
- 3.Compare: the means are equal, but Athlete A has the smaller range
Answer: Athlete A is more consistent
Avoid These
The most common mistakes students make.
Subtracting in the wrong order, giving a negative range instead of largest minus smallest.
When reading the range from a frequency table, using the frequency column instead of the actual data values.
When finding a missing value from a known range, not checking whether the missing value is the highest or the lowest, and adding or subtracting the range the wrong way round.
Assuming a larger range means a data set is more consistent, when actually a smaller range shows the data is more closely grouped together.
On questions that ask for both the mean and the range, only calculating one of them, when a full comparison of consistency needs both values stated.
FAQ
Questions parents and students ask.
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