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S3.5StatisticsCore

Comparing Data

Comparing two data sets is an exam staple. The rule is simple: compare a measure of location and a measure of spread, then interpret both in the context of the question.

20 min Representations of Data
Edexcel Statistics Y1 — Representations of Data playlist (Zeeshan Zamurred)Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Compare data sets using location and spread
  • Pick matching measures for a fair comparison
  • Interpret comparisons in context
  • Choose mean/SD vs median/IQR appropriately
1

Location and spread

A good comparison always covers two\textbf{two} things: a measure of location\textbf{location} (which set is higher on average) and a measure of spread\textbf{spread} (which set is more consistent). One without the other is incomplete.

compare: location+spread, in context\text{compare: location} + \text{spread, in context}
Always two comparisons, always contextual.
2

Matching measures

Use the same\textbf{same} measures for both sets. If the data has outliers, use the median and IQR (robust); if it is roughly symmetric with no outliers, the mean and standard deviation are fine — but be consistent across both sets.

Tip — Outliers → median & IQR. Symmetric, clean data → mean & standard deviation. Never mix measures across the two sets.

3

Interpreting in context

Always phrase conclusions using the situation. “The mean mark for Class A (62) is higher than Class B (55), so A performed better on average; A’s smaller standard deviation means its marks were more consistent.”

Example 1A: mean 62, SD 5. B: mean 55, SD 12. Compare.
1Location: A higher mean.
2Spread: A smaller SD (more consistent).
AnswerA is higher on average and more consistent

Formula recap

location+spread\text{location} + \text{spread}
Two comparisons every time.
outliers⇒median, IQR\text{outliers} \Rightarrow \text{median, IQR}
Robust measures.
symmetric⇒mean, SD\text{symmetric} \Rightarrow \text{mean, SD}
When data is clean.

Common mistakes to avoid

Comparing only the averages.
Also compare spread — and interpret both in context.
Using the mean for one set and the median for the other.
Use the same measures for a fair comparison.

Key takeaways

  • Compare a location measure AND a spread measure.
  • Use matching, appropriate measures (median/IQR if outliers; mean/SD if symmetric).
  • Always interpret the comparison in context.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Check your understanding

Work through questions on Comparing Data. Use the feedback to decide what needs another look.

1 past-paper question · 2 marks

Practise this topic

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