By Consumer Dummies

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]

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?

    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 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?

    Answer: City 2

    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?

    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.

  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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