Question

reading and interpreting box - and - whisker plots. the box - and - whisker plots to the left show the ticket sales, in millions of dollars, of the top 25 movies in 2000 and 2007 (for the united states only). answer the following questions a - d. a. which data set has a greater median? explain. b. which data set has a greater interquartile range? explain. c. about how much more were the ticket sales for the top movie in 2007 than for the top movie in 2000? d. what would be the benefit of using just one number line for both box - and - whisker plots?

Explanation:

Step1: Recall box - and - whisker plot properties

The line inside the box represents the median. In the box - and - whisker plot for 2007, the median line is at a higher value on the vertical axis (ticket sales in millions of dollars) compared to 2000. So 2007 has a greater median.

Step2: Recall inter - quartile range concept

The inter - quartile range (IQR) is the length of the box (Q3 - Q1). The box for 2007 is longer than the box for 2000, so 2007 has a greater inter - quartile range.

Step3: Calculate difference in median sales

The median for 2000 is around 150 million dollars and for 2007 is around 225 million dollars. The difference is \(225 - 150=75\) million dollars. So the ticket sales for the top movie in 2007 were about 75 million dollars more than in 2000.

Step4: Understand benefit of box - and - whisker plot

A box - and - whisker plot shows the spread and skewness of data, the median, the first and third quartiles, and any outliers. It gives a quick visual summary of the distribution of the data.

Answer:

A. The data set for 2007 has a greater median because the line inside the box for 2007 is at a higher value on the vertical axis.
B. The data set for 2007 has a greater inter - quartile range because the box for 2007 is longer.
C. The ticket sales for the top movie in 2007 were about 75 million dollars more than in 2000.
D. The benefit of using a box - and - whisker plot is that it shows the spread and skewness of data, the median, the first and third quartiles, and any outliers, giving a quick visual summary of the distribution of the data.