Back to Compare center and spread of data sets — Problem 5 · Task Set 2

Exercises: Comparing Center and Spread of Data Sets

Work through each section in order. Report center and spread as matched pairs: mean travels with standard deviation (SD), median travels with the interquartile range (IQR). Choose the pair by the SHAPE of the data first: roughly symmetric uses mean/SD; skewed or outlier-laden uses median/IQR. A complete comparison of two or more sets states a center finding AND a spread finding. Round SD to two decimal places unless told otherwise.

Grade 9·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-id-a-2

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Fluency Practice

Compute each statistic. Keep mean with SD and median with IQR.

A data set is $10, 12, 13, 14, 15, 16, 17, 19$ . The largest value is then changed from $19$ to $90$ . Which spread statistic changes the MOST?

The range, because it depends only on the maximum and minimum.

The IQR, because it changes whenever any value changes.

Neither — both the range and the IQR stay exactly the same.

The IQR, because it uses every value in the set.