Comparing Measures of Center and Variability

The double box plot below shows the number of car shows attended by two car clubs each year. Compare the centers and variations of the two populations.

• The Cruisers' IQR is 5 greater than the Car Hops' IQR.

• The Car Hops' IQR is 2 greater than the Cruisers' IQR.

• The data for the Car Hops is more consistent.

• The data for the Cruisers is more consistent.

The double box plot shows the heights in inches for the players on two professional basketball teams.

• While the median heights are about the same, the variation in heights is greater for the NJ Nets than the NY Knicks.

• While the median heights are about the same, the variation in heights is greater for the NY Knicks than the NJ Nets.

• The heights of the NJ Nets are more consistently centered around the median.

• The heights of the NY Knicks are less consistently centered around the median.

Which measure might be misleading in describing the value of each item?

• The mode, because it is significantly higher than the average.

• The mean, which gives an average value for the items.

• The mean, because of the outlier.

• The mode, because it is lower than the average.

The double box plot shows the average monthly high temperatures for Phoenix, Arizona, and Las Vegas, Nevada.

• Las Vega temperatures show greater variability than Phoenix.

• Phoenix temperatures show greater variability than Las Vegas.

• Las Vegas temperatures are more consistently centered around the median.

• Phoenix has a greater temperature range than Las Vegas.

Which measure of center and variability should you use to to compare these data sets? Choose one of each.

• Mean

• Median

• Standard Deviation

• IQR

What conclusion can Ms. Long make about the performance of her first- and second-period classes?

• The first-period class had a higher median score than the second-period class.

• The second-period class scores had a higher mean than the first-period class scores.

• The first-period class scores had a greater range than the second-period class scores.

• The second-period class scores had a greater mean absolute deviation than the first-period class scores.

The heights, in feet, of random samples of trees from three forests are shown.

Move each measure into the table to identify which forest is expected to have the greatest measure of center and which forest is expected to have the greatest measure of variability based on the samples.

a

b

c

greatest measure of center

-

greatest variability

Which measurements would represent the BEST measures of center & variability for the data set shown?

• Mean

• Median

• IQR

• Range

Which measure is the same in both classes?

• Median

• Lower Quartile

• Range

• Interquartile Range

Which measure of variability should you use?

• IQR

• standard deviation