Comparing Data Sets
How do I compare two data sets?
- You may be given two sets of data that relate to a context
- To compare data sets, you need to
- compare their averages
- Mode, median or mean
- compare their spreads
- Range
- compare their averages
How do I write a conclusion when comparing two data sets?
- When comparing averages and spreads, you need to
- compare numbers
- describe what this means in real life
- Copy the exact wording from the question in your answer
- There should be four parts to your conclusion
- For example:
- "The median score of class A (45) is higher than the median score of class B (32)."
- "This means class A performed better than class B in the test."
- "The range of class A (5) is lower than the range of class B (12)."
- "This means the scores in class A were less spread out than scores in class B."
- Other good phrases for lower ranges include:
- "scores are closer together"
- "scores are more consistent"
- there is less variation in the scores"
- For example:
What restrictions are there when drawing conclusions?
- The data set may be too small to be truly representative
- Measuring the heights of only 5 pupils in a whole school is not enough to talk about averages and spreads
- The data set may be biased
- Measuring the heights of just the older year groups in a school will make the average appear too high
- The conclusions might be influenced by who is presenting them
- A politician might choose to compare a different type of average if it helps to strengthen their argument!
What else could I be asked?
- You may need to choose which, out of mode, median and mean, to compare
- Check for extreme values (outliers) in the data
- Avoid using the mean as it is affected by extreme values
- Check for extreme values (outliers) in the data
- You may need to think from the point of view of another person
- A teacher might not want a large spread of marks
- It might show that they haven't taught the topic very well!
- An examiner might want a large spread of marks
- It makes it clearer when assigning grade boundaries, A, B, C, D, E, ...
- A teacher might not want a large spread of marks
Exam Tip
- When comparing data sets in the exam, half the marks are for comparing the numbers and the other half are for saying what this means in real life.
Worked example
Julie collects data showing the distances travelled by snails and slugs during a ten-minute interval. She records a summary of her findings, as shown in the table below.
| Median | Range | |
| Snails | 7.1 cm | 3.1 cm |
| Slugs | 9.7 cm | 4.5 cm |
Compare the distances travelled by snails and slugs during the ten-minute interval.
Compare the numerical values of the median (an average)
Describe what this means in real life
Slugs have a higher median than snails (9.7 cm > 7.1 cm)
This suggests that, on average, slugs travel further than snails
Compare the numerical values of the range (the spread)
Describe what this means in real life
Snails have a lower range than slugs (3.1 cm < 4.5 cm)
This suggests that there is less variation in the distances travelled by snails
