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.
Warm-Up: Describing and Comparing Distributions
These problems review description vocabulary you already know.
A data set has nine values clustered near 50 and one extreme value of 500. Adding the extreme value strongly changes one center but barely changes the other. Which center changes a lot: the ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ? Which center barely changes: the ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ? (Answer "mean" or "median" in each blank.)