Comparing Three Box Plots
The sample statistics questions here require that you compare three box plots. These sidebyside box plots represent home sale prices (in thousands of dollars) in three cities in 2012.
Sample questions

From high to low, what is the order of the cities’ median home sale prices?
Answer: City 2, City 1, City 3
The bar in the center of the box represents the median of each distribution; City 2 is the highest, followed by City 1 and City 3.

If the number of homes sold in each city is the same, which city has the greatest percentage of homes that sold for more than $72,000?
Answer: City 2
To find the percentage of homes in a city that sold for more than $72,000, look at the numerical axis, where you can see that City 2 has 75% of the data lying past 72 (because Q_{1} for City 2 is greater than 72). The other cities don’t.

Assuming 100 homes sold in each city in 2012, which city has the most homes that sold for more than $72,000?
Answer: City 2
The lower edge of the box, which represents Q_{1}, is above 72 for City 2, whereas the medians for City 1 and City 3 are below 72. Therefore, if all three cities had the same number of home sales in 2012, City 2 must have had the most above $72,000.

Which city has the smallest range in home prices?
Answer: City 1
The range is the maximum value minus the minimum value of a data set (shown in the very top line and the very bottom line of the box plot).
City 1 range: 80,000 – 62,000 = 18,000
City 2 range: 125,000 – 43,000 = 82,000
City 3 range: 80,000 – 38,000 = 42,000
City 1 has the smallest range, $18,000.

Which of the following statements is true?
(A) More than half of the homes in City 1 sold for more than $50,000.
(B) More than half of the homes in City 2 sold for more than $75,000.
(C) More than half of the homes in City 3 sold for more than $75,000.
(D) Choices (A) and (B).
(E) Choices (B) and (C).
Answer: D. Choices (A) and (B) (More than half of the homes in City 1 sold for more than $50,000; more than half of the homes in City 2 sold for more than $75,000.)
As indicated by the median lines within the boxes for each city, more than half of the homes in City 1 sold for more than $50,000, and more than half of the homes in City 2 sold for more than $75,000.

Which of the following statements is true?
(A) About 25% of homes in City 1 sold for $75,000 or more.
(B) About 25% of homes in City 2 sold for $75,000 or more.
(C) About 25% of homes in City 2 sold for $98,000 or more.
(D) About 25% of homes in City 3 sold for $75,000 or more.
(E) Choices (A) and (C).
Answer: E. Choices (A) and (C) (About 25% of homes in City 1 sold for $75,000 or more; about 25% of homes in City 2 sold for $98,000 or more.)
The cutoff for the upper 25% of the values in a box plot is indicated by the largest number in the box. For City 1, about 25% of homes sold for $75,000 or more, and about 25% of homes in City 2 sold for $100,000 or more.
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