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.
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 things: a measure of (which set is higher on average) and a measure of (which set is more consistent). One without the other is incomplete.
Matching measures
Use the 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.”
Formula recap
Common mistakes to avoid
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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