Comparing Data Sets (Cambridge (CIE) IGCSE International Maths)

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, ...