Question

unit 5 discussion sale data comparison reading and interpreting box - and - whisker plots the number of runs scored 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 concepts

The line inside the box represents the median. The length from Q1 (lower quartile) to Q3 (upper quartile) is the inter - quartile range (IQR).

Step2: Compare medians

For the 2000 box - and - whisker plot, the median is around 125. For the 2007 box - and - whisker plot, the median is around 175. So 2007 has a greater median.

Step3: Compare inter - quartile ranges

The length of the box for 2000 (IQR) is from about 100 to 150 (IQR = 50). The length of the box for 2007 (IQR) is from about 150 to 250 (IQR = 100). So 2007 has a greater inter - quartile range.

Step4: Analyze ticket sales

The minimum value for 2000 is around 75 and for 2007 is around 100. The maximum value for 2000 is around 250 and for 2007 is around 325. The difference in maximum values gives an idea of how much more ticket sales there were. \(325 - 250=75\) million dollars more in 2007.

Step5: Advantage of one number

Using the median would be beneficial as it is less affected by outliers. It gives a measure of the central tendency that represents the middle value of the data set.

Answer:

A. The 2007 data set has a greater median because the line inside the box (median) for 2007 is at a higher value (around 175) compared to 2000 (around 125).
B. The 2007 data set has a greater inter - quartile range. The length of the box (from Q1 to Q3) is larger for 2007 (from about 150 to 250, IQR = 100) than for 2000 (from about 100 to 150, IQR = 50).
C. The ticket sales for the top movie in 2007 were about 75 million dollars more than in 2000 (325 - 250 = 75), by comparing the maximum values of the two box - and - whisker plots.
D. The median would be the most beneficial one number to use as it is less influenced by extreme values (outliers) and gives a good representation of the central value of the data set.