Using Measures of Dispersion (Edexcel GCSE Statistics)

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 an average (measure of central tendency)

    • Mode, median or mean

  • AND compare a measure of spread (measure of dispersion)

    • Range or interquartile range (IQR)

• You need to use the same average and the same measure of spread for both data sets

• You may need to decide which average should be used

  • See the 'Using Measures of Central Tendency' revision note

• Which measure of spread to use depends on which average is used

  • If you compare the modes of the data sets

    • then use the range (quantitative data only)

  • If you compare the medians of the data sets

    • then use the range or interquartile range

    • interquartile range is the most common choice

  • If you compare the means of the data sets

    • then use the range

    • interquartile range should not be used with mean

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 the context of the question ('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 that, on average, 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 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, ...

• You may be asked to compare data from a sample with data from the population as a whole

  • For example, to determine how representative the sample is of the population