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S-ID.2 Warmup M1-051-A10-V04

Compare data sets using center and spread measures appropriate to distribution shape.

Decide which group has more variability

Problem

Compare the variability in books read last month for class 1, with \(IQR~6\) and \(\text{range}~14\), and class 2, with \(IQR~9\) and \(\text{range}~14\). Explain the total-spread and middle-half-spread conclusions.

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The classes have the same variability because both ranges are 14.

Both classes have range 14, so their total spread is the same, but Class 2 has more middle-half spread because its IQR is 9 instead of 6.

Class 2 has more variability by both range and IQR because 9 is greater than 6.

Class 1 has more variability because its IQR is smaller, so the data are more spread out.

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Curriculum context

Course: Math I
Standard: S-ID.2
Category: Statistics and Probability
Domain: Interpreting Categorical and Quantitative Data
Objective: Compare data sets using center and spread measures appropriate to distribution shape.
Problem type: Decide which group has more variability