Sheet № 244 · Foundation + Higher · AQA · Edexcel · OCR
Comparing Data Sets –
Comparing data sets is one of the most frequently tested skills on GCSE Maths papers at both Foundation and Higher tier. AQA, Edexcel and OCR all require you to compare two distributions using an average and a measure of spread — and to write your comparisons in context. Many students lose marks not because they cannot calculate the stati
§Key definitions
Question:
Class A scored a mean of 62 marks and a range of 45 marks on a test. Class B scored a mean of 58 marks and a range of 30 marks. Compare the two classes.
Average:
Class A has a higher mean (62 vs 58), so on average Class A scored higher on the test.
Spread:
Class A has a larger range (45 vs 30), so Class A's marks were more spread out. Class B's marks were more consistent.
Answer:
On average, Class A performed better because their mean is higher (62 compared to 58). However, Class B was more consistent because their range is smaller (30 compared to 45).
Q1 (Foundation):
Team A: mean = 3.2 goals per match, range = 6. Team B: mean = 2.8 goals per match, range = 3. Compare the two teams.
§Formulas to memorise
Mean = sum of all values ÷ number of values
Range = highest value − lowest value
IQR = Q3 − Q1
Calculate or read off — the relevant average for each data set (mean or median).
Calculate or read off — the relevant measure of spread for each data set (range or IQR).
Compare the averages — state which is higher/lower and what this means in context.
Compare the spread — state which is larger/smaller and what this means in context (e.g. more consistent, more varied).
Use sentence starters — such as "On average, Group A scored higher because their median is ..." and "Group B's results were more consistent because their IQR is smaller."
Worked example
Class A scored a mean of 62 marks and a range of 45 marks on a test. Class B scored a mean of 58 marks and a range of 30 marks. Compare the two classes.
Working:
⚠ Common mistakes
- ✗Only comparing one measure. You must compare both an average AND a measure of spread to earn full marks.
- ✗Not using context. Saying "Group A is higher" is not enough. Say "Group A scored higher on the test" or "Factory Y completed the task more quickly."
- ✗Using different measures for each group. Compare like with like — use the median for both groups, not the mean for one and the median for the other.
- ✗Confusing spread with average. A larger range does not mean a higher average — it means more variability.
✦ Exam tips
- →If the question gives you box plots, use the median and IQR (not the mean and range).
- →If the question gives you raw data, calculate the mean or median and the range or IQR for both data sets.
- →Always make two separate, clearly labelled comparison points.
- →Use linking words: "therefore", "which suggests", "meaning that".
- →For box plot skills, see cumulative frequency and box plots. For averages, see mean, median, mode and range.