Pre-Algebra
Data and graphs
Comparing data distributions
20 practice questions
0 video lessons
Theory + worked examples
Comparing Data Distributions
California Pre-Algebra • Standard 7.SP.3 • Data & Graphs
Comparing Data Distributions is a topic in Data & Graphs in the California Common Core State Standards. It is aligned to Standard 7.SP.3, which requires students to compare two data distributions by center, spread, and shape.
Comparing data sets means comparing their centers, spreads, and shapes, often with side-by-side box plots.
Theory
Comparing distributions looks at differences in center (median), spread (IQR, range), and shape.
Side-by-side box plots make the comparison visual.
Two box plots compared.
What to compare.
Compare:
\[\text{center, spread, and shape}\]
Use the median and IQR for skewed data.
How to compare distributions
- Compare the medians (centers).
- Compare the IQRs or ranges (spreads).
- Note the shapes and any overlap.
- Draw a conclusion in context.
Example 1 — Higher center
Group A median \(8\), Group B median \(12\). Which is higher?
Solution
Group B has the larger median.
Example 2 — Compare spread
A: IQR \(6\); B: IQR \(6\). Which is more spread?
Solution
Equal IQRs — same middle-half spread.
Example 3 — Overlap
Why compare distributions, not single values?
Solution
To see typical values and variability together.
Example 4 — Which typically higher
If B's whole box is right of A's, what does that mean?
Solution
B's values are typically higher.
Common pitfalls
Compare both center and spread, not just one.
Use the median for skewed data.
A higher box means typically larger values.
Frequently asked questions
How do I compare two data sets?
Compare their center, spread, and shape.
What shows the center?
The median.
What shows the spread?
The IQR or range.
Why use box plots?
They compare distributions visually.
← Previous subtopic
Measures of spread (range, IQR, MAD)
Next subtopic →
Scatter plots and bivariate data
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