Compare multiple distributions using measures of center and spread.
Compare two data sets by their center and spread to tell which group is typically higher or more consistent.
核心知识
When comparing two data sets, use center (mean or median) to see which group has higher or lower typical values, and use spread (range, IQR, or standard deviation) to see which group is more consistent or more variable.
深入理解
The SAT often shows two box plots, two dot plots, or a table with summary statistics for two groups, then asks you to compare them.
Center comparison is straightforward: whichever group has a higher mean or median has higher typical values.
Spread comparison tells you about consistency. A smaller IQR or standard deviation means the values cluster more tightly — the data is more predictable. A larger spread means more variability.
Match the comparison to the question. If it asks "which class performed better on average," compare means or medians. If it asks "which class had more consistent scores," compare IQR or standard deviation.
Watch for questions that combine both: "Class A had a higher median but also a larger IQR than Class B." That means Class A's typical score was higher, but its scores were more spread out.
分步讲解
- Identify the center measure (mean or median) for each group.
- Identify the spread measure (range, IQR, or SD) for each group.
- Compare centers to determine which group has higher/lower typical values.
- Compare spreads to determine which group is more/less consistent.
- Read the question stem carefully — it might ask about center, spread, or both.
常见误解
- Assuming a higher median automatically means every value in that group is higher — the distributions can overlap significantly.
- Confusing a wider box in a box plot with a higher center — width is spread, not center.
- Using range to compare consistency when IQR or SD would be more appropriate (range is heavily influenced by a single extreme value).
示例解析
Two classes took the same quiz. Class A has a median score of 78 and an IQR of 12. Class B has a median score of 82 and an IQR of 6. Which statement is best supported?
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