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 Video by Zeeshan Zamurred Representations of Data

Edexcel Statistics Y1 — Representations of Data playlist (Zeeshan Zamurred)Watch the full walkthrough 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

Location and spread

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

compare: location + spread, in context

Always two comparisons, always contextual.

Matching measures

Use the $same$ 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.

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.”

1Location: A higher mean.

2Spread: A smaller SD (more consistent).

AnswerA is higher on average and more consistent

Formula recap

location + spread

Two comparisons every time.

outliers \Rightarrow median, IQR

Robust measures.

symmetric \Rightarrow 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

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