Comparing Data Sets
To compare two data sets, use an average (mean, median or mode) to compare a typical value and the range to compare how spread out the data is.
When comparing two data sets — for example, test scores from two classes — you need two things:
- An average (mean, median or mode) to compare where the data is centred — which group did better on average?
- The range to compare how spread out the data is — which group was more consistent?
For example, if Class A has a higher mean but also a larger range, you might say: "On average Class A scored higher, but Class B was more consistent."
Always state your comparisons in context — refer to what the data actually represents, not just the numbers.
Change the data set below to explore how the averages and range differ between Set A and Set B.
Watch it work
Question: Two classes sit the same test (out of 50).
Class A:
Class B:
Compare the two classes.
Step 1 (Averages):
Class A mean:
Class B mean:
Step 2 (Ranges):
Class A range:
Class B range:
Step 3 (Comparison): On average Class A scored slightly higher (mean 37 vs 36). However, Class B was much more consistent (range 4 vs 17), meaning their scores were closer together.
Have a go
Q1. Team X has a mean score of 14 and a range of 8. Team Y has a mean score of 12 and a range of 3. Which team is better on average? Which is more consistent?
Team X has a higher mean, so it is better on average. Team Y has a smaller range, so it is more consistent.
Q2. Set P: . Set Q: . Find the mean and range of each set and compare them.
Set P mean = , range = .
Set Q mean = , range = .
Both sets have the same mean (5), but Set P has no spread (range 0) while Set Q is very spread out (range 8). The averages alone do not show how different the data sets are — the range reveals it.
Q3. Ali's last 5 homework scores: . Ben's last 5 homework scores: . Who should the teacher be more concerned about? Use averages and range to explain.
Ali: mean = 7, range = .
Ben: mean = 7, range = 0.
Both average 7, but Ali's scores vary — some are high and some low. Ben is perfectly consistent. The teacher might want to check why Ali's scores fluctuate.
Q4. Why is it not enough to compare only the means of two data sets?
Two data sets can have the same mean but very different spreads. You need the range (or another measure of spread) to get a full picture of how the data is distributed.