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First teaching 2021

Last exams 2024

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Comparing Distributions (CIE IGCSE Maths: Extended)

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Comparing Distributions

What does comparing distributions mean?

  • Many questions will give you data that has been split into two related categories
  • e.g.  Data about daily screen time by children and adults
    • the data is all about screen time but has been split into two distributions
      • one for children
      • one for adults
  • To compare distributions you should look to compare two things
    • the average of the distributions
    • the spread (variation) of the distributions

How do I compare the averages of two data sets (distributions)?

  • Choose the appropriate average (mode, median or mean)
    • The mean includes all the data
    • The median is not affected by extreme values
    • The mode can be used for non-numerical data
  • Consider whether it is better for the average to be bigger or smaller
    • If you are comparing time to complete a puzzle - the smaller the average the better
    • If you are comparing test scores - the bigger the average the better
  • Give numerical values for the average and explicitly compare
    • e.g. The mean for dogs is 17 kg which is bigger than the mean for cats which is 13 kg
  • Give your comparison in context
    • e.g. The mean for dogs is bigger which suggests that, on average, dogs are heavier than cats

How do I compare the spread (variation) of two data sets (distributions)?

  • Choose the appropriate range (range or interquartile range)
    • The range is affected by extreme values
    • The interquartile range focuses on the middle 50%
  • Consider whether it is better for the range to be bigger or smaller
    • A smaller range implies consistency
    • A bigger range implies more spread
  • Give numerical values for the range and explicitly compare
    • e.g. The interquartile range for dogs is 6 kg which is bigger than the interquartile range for cats which is 4 kg
  • Then give your comparison in context
    • e.g. The interquartile range for cats is smaller which suggests that the weights of cats are more consistent and less spread out than dogs
  • When comparing raw data sets, you may also need to check for outliers in either distribution
    • If one, or both, of the data sets has a data value that is much larger or smaller than the others, this may need mentioning and a possible reason given 

Worked example

Julie collects data on the distances travelled by snails and slugs over the duration of ten minutes. She records a summary of her findings as shown in the table below.

  Median Interquartile range
Snails 7.1 cm 3.1 cm
Slugs 9.7 cm 4.5 cm

Compare the distances travelled by snails and slugs over the duration of ten minutes.

For average, compare medians - remember to comment with numbers, then in context.

Slugs have the higher median (9.7 > 7.1) which suggests that on average slugs move further than snails

For spread, compare interquartile ranges - again, comment with numbers, then in context.

Snails have the lower interquartile range (3.1 < 4.5) which suggests that there is less variation in the distances travelled by snails

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.