Comparing Distributions | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What does comparing distributions mean?

• Many questions present data divided into two related categories.
• For example, data on daily screen time for children and adults:
• The data pertains to screen time but is divided into two distributions:
  • One for children.
  • One for adults.
• To compare these distributions, you should examine two aspects:
  • 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 considers all data points.
  • The median is not influenced by extreme values.
  • The mode is suitable 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:
  • For example, The mean for dogs is 17 kg which is bigger than the mean for cats which is 13 kg.
• Give your comparison in context:
  • For instance, 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)?

• Select the appropriate measure of range (range or interquartile range):
  • The range is influenced by extreme values.
  • The interquartile range (IQR) focuses on the middle 50% of the data.
• Consider whether a larger or smaller range is preferable:
  • A smaller range indicates consistency.
  • A larger range indicates more spread.
• Provide numerical values for the range and make explicit comparisons:
  • For example, "The IQR for dogs is 6 kg, which is larger than the IQR for cats at 4 kg."
• Contextualize your comparison:
  • For example, "The smaller IQR for cats suggests their weights are more consistent and less spread out compared to dogs."
• When comparing raw data sets, check for outliers in either distribution:
  • If one or both data sets contain values significantly larger or smaller than the rest, mention this and consider possible reasons.