Comparing two data sets means using a measure of average (mean, median, or mode) to compare the typical value in each group, and a measure of spread (range) to compare how consistent the values are. A full comparison always makes two separate statements and links both back to the real-life context of the question.
Why do you need both an average and a measure of spread?
An average alone can be misleading. Two groups might have the same mean but very different patterns — one could be tightly clustered around the average, while the other has wild extremes.
Example: Two students' last five test scores:
| Student | Scores | Mean | Range |
|---|---|---|---|
| Alex | 55, 58, 60, 62, 65 | 60 | 10 |
| Jamie | 20, 40, 60, 80, 100 | 60 | 80 |
Both have a mean of 60, but Alex is far more consistent (range 10 vs range 80). An examiner who only looked at the mean would miss this crucial difference.
How do you choose between mean and median?
- Use the mean when data has no extreme outliers — it uses every value and is precise.
- Use the median when there are outliers or the data is skewed — it is not dragged by extreme values.
In KS3 comparisons, questions usually specify "use the mean" or "use the median." If not specified, state which you are using and why.
What are the steps for comparing two data sets?
Step 1: Calculate the chosen average (mean or median) for each data set.
Step 2: Calculate the range for each data set. Range = highest value − lowest value.
Step 3: Write a statement comparing the averages, mentioning which is higher and what that means in context.
Step 4: Write a statement comparing the ranges, mentioning which is larger and what that means in context.
Step 5: (If asked) Make an overall conclusion.
Worked example:
Class A reaction times in milliseconds: 210, 230, 240, 250, 270 Class B reaction times in milliseconds: 180, 200, 250, 290, 330
| Class A | Class B | |
|---|---|---|
| Mean | (210+230+240+250+270)÷5 = 1200÷5 = 240 ms | (180+200+250+290+330)÷5 = 1250÷5 = 250 ms |
| Range | 270−210 = 60 ms | 330−180 = 150 ms |
Comparison statement (average): Class A has a lower mean reaction time (240 ms vs 250 ms), so on average Class A reacted more quickly.
Comparison statement (spread): Class A has a smaller range (60 ms vs 150 ms), so Class A's reaction times are more consistent — their performance is more reliable.
How do you write a good comparison statement?
A good comparison statement does three things:
- States the value for each group (not just "Class A's mean is higher" — write the actual numbers).
- States which is larger/smaller.
- Interprets what that means in the context of the question.
Poor answer: "Class A's mean is less than Class B's mean."
Better answer: "Class A's mean reaction time (240 ms) is lower than Class B's (250 ms), suggesting Class A reacted more quickly on average."
If a question says "use the data to compare the performance of the two classes," it expects both an average comparison and a range comparison — one sentence each is usually enough.
What other measures of spread might you meet?
At KS3, range is the main spread measure. The calculation is always:
Range = largest value − smallest value
At GCSE, you will also use the interquartile range (IQR) = upper quartile − lower quartile, which is less affected by outliers than the range. For KS3 purposes, the range is sufficient unless your teacher or the question states otherwise.
Frequently asked questions
Do I have to calculate the average or can I just quote it from a diagram?
If the mean or median is given in the question or shown on a diagram (for example, on a stem-and-leaf plot), you can quote it directly — you do not need to recalculate it. Always show any calculation you do perform, even if brief.
What if one data set has more values than the other?
The mean and range still work fine regardless of different set sizes, because the mean divides by the count for each group separately. However, a larger data set generally gives a more reliable estimate of the true average. You can mention this in your conclusion if relevant.
Can I use the mode to compare data sets?
The mode is the least useful average for comparisons because many data sets have no mode or several modes. Use mean or median for comparisons unless the question specifically asks for the mode.
What does it mean if two data sets have the same mean but different ranges?
It means the typical value is similar, but the consistency is different. A smaller range means values are clustered closely around the average (more predictable). A larger range means values are spread out (less predictable). In an exam, mention both the similarity and the difference.
For Socratic KS3 statistics practice comparing data sets with Professor Pi, see aitutors.me.