Comparing Data Sets (Edexcel IGCSE Maths A (Modular))
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
Comparing Distributions
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
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"
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
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, ...
Examiner Tips and Tricks
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
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