Describing 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 below shows the results of a school survey about types of lunch purchased.

• The a la carte data have less variation than full lunch.

• The a la carte data are centered around a higher value.

• The data for full lunch has a median of 180.

• The data for a la carte lunches has an interquartile range of 240 students.

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 dot plot shows the number of city pet registrations for several days.

• The mean number of cat registrations is greater than the mean number of dog registrations.

• The dogs’ data has a mean of 10 registrations.

• The cats’ data has a mean of 15 registrations.

• The mean number of dog registrations is greater than the mean number of cat registrations.

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 variability

-

greatest measure of center

The best description of the data is ​ (a)   . ​ ​ The most appropriate measure of center is the​ (b)   . The most appropriate measure of variability is the ​ (c)   .

​

• range

• mean

• IQR

• median

• skewed right

• symmetric

• symmetric with an outlier

• skewed left

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 variability

greatest measure of center

-

The best description of the data is ​ (a)   . ​ ​ The most appropriate measure of center is the​ (b)   . The most appropriate measure of variability is the ​ (c)   .

• range

• mean

• IQR

• median

• skewed right

• symmetric

• symmetric with an outlier

• skewed left

The best description of the data is ​ ​ (a)   . ​ The most appropriate measure of center is the​ ​ (b)   . The most appropriate measure of variability is the ​ ​ (c)   .

• range

• mean

• skewed left

• mean

• range

• skewed right

• symmetric

• symmetric with an outlier

The best description of the data is ​ ​ (a)   . ​ ​ The most appropriate measure of center is the​ ​ (b)   . The most appropriate measure of variability is the ​ ​ (c)   .

• range

• mean

• skewed left

• median

• IQR

• skewed right

• symmetric

• symmetric with an outlier