Back to Exercise: Compare center and spread of data sets

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

Printable layout

Warm-Up: Mean, Median, and the Five-Number Summary

These problems review computations you already know from HSS.ID.A.1.

A data set is $4, 6, 8, 10, 12$ . What is the mean?

$8$

$10$

$6$

$40$

For the ordered data set $4, 6, 8, 10, 12$ , what is the median?

$8$

$7$

$10$

$6$

A data set has five-number summary minimum $= 10$ , $Q_1 = 14$ , median $= 18$ , $Q_3 = 24$ , maximum $= 30$ . Compute the IQR.

Fluency Practice

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

Compute the standard deviation of $4, 6, 8, 10, 12$ (mean $= 8$ ). Use the population formula (divide the sum of squared deviations by $n = 5$ ). Round to two decimal places.

A second set is $7, 7, 8, 9, 9$ . Its mean is also $8$ . Without the long computation, which set is MORE spread out: this one or $4, 6, 8, 10, 12$ ? Then state the larger standard deviation rounded to two decimals (it is $2.83$ for one set and $0.89$ for the other). Enter only the larger SD.

Set $X$ has mean $50$ and SD $4$ . Set $Y$ has mean $50$ and SD $12$ . What can you conclude?

The two sets have the same center, but $Y$ is more spread out (more variable) than $X$ .

$Y$ has larger values than $X$ , because its SD is bigger.

$Y$ is a better data set than $X$ , because a bigger SD is better.

$X$ has a higher center than $Y$ , because its SD is smaller.

$A dot plot of books read with values 2, 3, 4, 4, 5, 6 forming a roughly symmetric mound with no outliers.$

The dot plot below shows the number of books $8$ students read over the summer. Describe the shape (roughly symmetric, or skewed/outlier-laden), then name the matched pair of statistics — center and spread — you would report for this data.

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.

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