Pre-Algebra
Probability (introductory)
Comparing two populations informally
20 practice questions
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Theory + worked examples
Comparing Two Populations Informally
California Pre-Algebra • Standard 7.SP.4 • Probability
Comparing Two Populations Informally is a topic in Probability in the California Common Core State Standards. It is aligned to Standard 7.SP.4, which requires students to informally compare two populations using center and spread.
Two populations are compared informally by their centers and spreads; a large center gap relative to spread signals a real difference.
Theory
Comparing two populations informally uses their centers (medians) and spreads (IQR).
A center gap that is large relative to the spread suggests a real difference.
Two populations compared.
What to look for.
Compare:
\[\text{center gap vs. spread}\]
Use medians and IQRs for the comparison.
How to compare informally
- Find the center of each population.
- Find the spread of each.
- Compare the center gap to the spread.
- Judge whether the difference is meaningful.
Example 1 — Which is higher
A median \(8\), B median \(13\). Which is typically higher?
Solution
Group B.
Example 2 — Meaningful gap
When is a difference in centers meaningful?
Solution
When it is large relative to the spread.
Example 3 — Informal
Why 'informally' compare?
Solution
We compare visually without a formal test.
Example 4 — Spread
What does a wider box mean?
Solution
More variability in that population.
Common pitfalls
A small gap with large spread may not be meaningful.
Compare spread too, not just centers.
This is informal, not a formal test.
Frequently asked questions
How do I compare two populations?
Compare their centers and spreads.
When is a difference meaningful?
When the center gap is large relative to the spread.
What shows the center?
The median.
What shows the spread?
The IQR.
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