Back to Interpret shape, center, and spread in context — Problem 4 · Task Set 3

Exercises: Interpret Shape, Center, and Spread in Context

Work through each section in order. For interpretation problems, write in complete sentences about the real-world quantity, not just numbers. Remember: skew points toward the TAIL, the median and IQR resist outliers while the mean and standard deviation do not, and "lower" or "higher" is good or bad only relative to what is being measured.

Grade 9·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-id-a-3

Work through problems with immediate feedback

Fluency Practice

Read each plot or summary and answer in context.

Two classes take the same exam. Class X has a higher mean score than Class Y. A student concludes "a higher mean is always better, so Class X did better." On a DIFFERENT measure — the number of errors on a typing test — Class X also has the higher mean. What is the correct reasoning?

Whether higher is better depends on the context: a higher exam score is good, but a higher error count is bad. You must check what is being measured first.

A higher mean is always better, so Class X is better on both measures.

A higher mean is always worse, so Class Y is better on both measures.

You can never compare two groups using their means.