Comparing Three Box Plots - dummies

# Comparing Three Box Plots

The sample statistics questions here require that you compare three box plots. These side-by-side box plots represent home sale prices (in thousands of dollars) in three cities in 2012.

Credit: Illustration by Ryan Sneed

## Sample questions

1. 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.

2. 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?

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 Q1 for City 2 is greater than 72). The other cities don’t.

3. Assuming 100 homes sold in each city in 2012, which city has the most homes that sold for more than \$72,000?

The lower edge of the box, which represents Q1, 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.

4. Which city has the smallest range in home prices?

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.

5. 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.

6. 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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