Exercise 15 Page 343

Practice makes perfect

a Consider the given box-and-whisker plot for the prices (in dollars) of entrées at a restaurant.

We are asked to find and interpret the range of the data set represented by the given figure. To do so, let's first find the least and greatest value of the data. The leftmost point on the box plot represents the least value, which is 8.75. The rightmost point represents the greatest value, which is 18.25. Let's calculate the difference of these values to find the range. Range: 8.75- 18.25=$9.50 This means that the prices of the entrées at the restaurant vary by no more than $9.50.

b In this part we are asked to describe the distribution of the data set. In a box-and-whisker plot, each whisker represents 25 % of the data. The box represents 50 % of the data. With this in mind, we can state the following facts about the distribution of the data.

25 % of the entrées cost between $8.75 and $10.50.
50 % of the entrées cost between $10.50 and $14.75.
25 % of the entrées cost between $14.75 and $18.25.

c The interquartile range (IQR) is given by the difference of the third quartile, Q_3, and the first quartile, Q_1. In a box-and-whisker plot, the left point of the right whisker represents Q_3, which is 14.75. The right point of the left whisker represents Q_1, which is 10.50. Let's calculate the difference of these values to find IQR.

IQR: 14.75- 10.50=$4.25 The interquartile range is $4.25. This means that the middle half of the prices of the entrées at the restaurant vary by no more than $4.25.

d To find if the data is more spread out below Q_1 or above Q_3, let's look at the whiskers to see which one is longer.

Since the right whisker is longer, the data above Q_3 is more spread out than the data below Q_1.

Subchapter links

Communicate Your Answer p.339

Monitoring Progress p.340-342

Exercise 15 Page 343

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