Comparing Data Sets
Comparing data sets means using averages (mean, median or mode) and a measure of spread (range or interquartile range) to describe how two or more sets of data are similar or different. A full comparison always makes two statements: one comparing the averages (which set has a higher or lower typical value) and one comparing the spread (which set is more consistent). This topic is tested throughout GCSE Statistics using diagrams like back-to-back stem-and-leaf diagrams and box plots as well as raw data.
Before you start
Make sure you're comfortable with these topics first:
Method
- Calculate the same average (usually the mean or median) for both data sets, using the same method for each so the comparison is fair.
- Calculate the same measure of spread (usually the range, or the interquartile range if quartiles are available) for both data sets.
- Write a comparison of the averages in context, stating which data set has the higher or lower typical value and what that means in the situation given.
- Write a comparison of the spread in context, stating which data set is more consistent (smaller spread) or more variable (larger spread).
- Always refer back to the context of the question (e.g. 'the boys' times' or 'class A's marks') rather than just giving numbers, since comparison marks are usually awarded for context.
- If given a diagram such as a box plot, read the median and quartiles/range directly off the diagram rather than recalculating from scratch.
Worked example
The times, in minutes, taken by 5 runners in Team A are: 22, 25, 23, 28, 22. The times taken by 5 runners in Team B are: 24, 24, 25, 26, 26. Compare the two teams' times using the mean and the range.
- Team A mean: 22+25+23+28+22 = 120, 120/5 = 24 minutes.
- Team B mean: 24+24+25+26+26 = 125, 125/5 = 25 minutes.
- Team A range: 28 - 22 = 6 minutes. Team B range: 26 - 24 = 2 minutes.
- Compare averages: Team A has a lower mean time (24 minutes) than Team B (25 minutes), so on average Team A were faster.
- Compare spread: Team A has a much larger range (6 minutes) than Team B (2 minutes), so Team B's times were more consistent.
- Final answer: Team A was faster on average (mean 24 vs 25 minutes) but less consistent (range 6 vs 2 minutes).
Practice questions
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Q1Class A has a mean test score of 62 and Class B has a mean of 58. Which class did better on average?Show answer
Answer: Class A (higher mean score)
Q2Data set X has a range of 12 and data set Y has a range of 5. Which data set is more consistent?Show answer
Answer: Data set Y (smaller range means less spread/more consistent)
Q3Team 1 has median height 165 cm and Team 2 has median height 172 cm. Write one comparison in context.Show answer
Answer: Team 2 players are taller on average (higher median height) than Team 1
Q4Shop A's daily sales have an IQR of 40 pounds and Shop B's have an IQR of 15 pounds. Which shop has more variable daily sales?Show answer
Answer: Shop A (larger IQR means more variable/spread out sales)
Q5The mean rainfall in April was 45 mm with a range of 20 mm; in May it was 45 mm with a range of 8 mm. Compare April and May.Show answer
Answer: The mean rainfall was the same in both months, but April was more variable (larger range) than May
Q6Two classes sit the same test. Class P: mean 70, range 10. Class Q: mean 55, range 30. Write a full comparison.Show answer
Answer: Class P scored higher on average (mean 70 vs 55) and was more consistent (smaller range, 10 vs 30)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
Two machines fill bottles with juice. Machine A's fill volumes (ml) have a mean of 500 and a range of 4. Machine B's fill volumes have a mean of 498 and a range of 20. Compare the two machines' fill volumes.
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The marks out of 50 for 9 students in Test 1 were: 30, 32, 35, 28, 40, 33, 31, 36, 29. In Test 2, the same 9 students scored: 25, 45, 20, 48, 22, 44, 30, 46, 25. (a) Calculate the mean mark for each test. (b) Calculate the range for each test. (c) Compare the two tests.
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A survey compares the number of hours of screen time on a school day for 10 Year 8 students (median 3.5 hours, IQR 1.2 hours) and 10 Year 11 students (median 4.8 hours, IQR 2.5 hours). Compare the screen time of the two year groups.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the comparing data sets worksheet pack - 20 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 6 of GCSE Statistics Foundation Workbook 2 and chapter 10 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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