Comparing distributions
Edexcel 1MA1 Papers 2 and 3 regularly ask you to compare two data sets or distributions. A comparison answer that just states numbers without interpretation scores only partial credit.
What to compare
Always address TWO aspects:
- A measure of average (mean, median, or modal class): tells you about the "typical" or "central" value of the distribution.
- A measure of spread (range, IQR, or standard deviation): tells you how consistent or variable the data is.
Language of comparison
Do NOT just write "Set A has a mean of 45 and Set B has a mean of 50." Write: "Set B has a higher mean score (50 > 45), suggesting students in Set B performed better on average."
Do NOT just write "Set A has an IQR of 12 and Set B has an IQR of 20." Write: "Set A has a smaller IQR (12 < 20), meaning Set A's scores are more consistent/less spread."
Choosing the right measure
Mean vs median:
- Use median when data contains outliers or is skewed.
- Use mean when data is roughly symmetrical and no extreme outliers.
Range vs IQR:
- IQR is preferred when outliers are present — it is not affected by extreme values.
- Range is simpler but sensitive to outliers.
Interpreting from cumulative frequency graphs
From a cumulative frequency graph you can read off:
- Median (at n/2)
- Q1 (at n/4), Q3 (at 3n/4) → IQR = Q3 − Q1
- Percentiles
Edexcel may ask you to draw two curves on one grid and compare them.
Box plots
A box plot displays: minimum, Q1, median, Q3, maximum. Comparing two box plots: comment on the median (average performance) and the box width (IQR → spread/consistency).
⚠Common mistakes
- No context: always relate back to what the data represents.
- Only comparing one aspect: you need both average AND spread.
- Saying "better" without explaining why: specify what "better" means in context.
- Confusing median position: for n values, the median is at position (n+1)/2 in a list, or at n/2 on a cumulative frequency graph.
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