Question

1. the following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. based on the boxplot, the top 25% of the cars have a typical gas mileage of at least how many miles per gallon? (a) 15 (b) 20 (c) 25 (d) 35 (e) 50

1. an amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. the following boxplot shows the heights of a sample of people who entered the amusement park on one day. based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction? (a) 25% (b) 48% (c) 50% (d) 75% (e) 100%

1. an airline recorded the number of on - time arrivals for a sample of 100 flights each day. the boxplot below summarizes the recorded data for one year. based on the boxplot, which of the following statements must be true?

(a) the range of the number of on - time arrivals is greater than 90.
(b) the interquartile range of the number of on - time arrivals is 22.
(c) the percent of days that had at least 80 on - time arrivals is greater than the percent of days that had at most 76 on - time arrivals.
(d) the percent of days that had from 76 to 80 on - time arrivals is equal to the percent of days that had at most 76 on - time arrivals.
(e) the difference between the median and the lower quartile for the number of on - time arrivals is less than 2.

Explanation:

Step1: Recall box - plot properties

In a box - plot, the right - hand side of the box represents the third quartile ($Q_3$), which means 75% of the data lies below it and 25% of the data lies above it.

Step2: Solve problem 4

For the gas - mileage box - plot, the value of $Q_3$ is 35. So the top 25% of the cars have a typical gas mileage of at least 35 miles per gallon. The answer to problem 4 is (d).

Step3: Solve problem 5

For the height box - plot, the value of 48 inches is at the median (the line inside the box). Since 50% of the data lies above the median, approximately 50% of the people who entered the amusement park met the height requirement. The answer to problem 5 is (c).

Step4: Solve problem 6

• For the on - time arrivals box - plot:
• The range is $100 - 70=30$, so (a) is false.
• The inter - quartile range ($IQR = Q_3 - Q_1$). If we assume $Q_1\approx76$ and $Q_3\approx88$, $IQR\approx88 - 76 = 12

eq22$, so (b) is false.

• The percent of days with at least 80 on - time arrivals is more than 50% (since 80 is close to $Q_3$), and the percent of days with at most 76 on - time arrivals is 25% (since 76 is close to $Q_1$). So (c) is true.
• The percent of days from 76 to 80 is not equal to the percent of days with at most 76 on - time arrivals, so (d) is false.
• The median is around 80 and $Q_1$ is around 76, and the difference is $80 - 76=4>2$, so (e) is false. The answer to problem 6 is (c).

Answer:

1. d. 35
2. c. 50%
3. c. The percent of days that had at least 80 on - time arrivals is greater than the percent of days that had at most 76 on - time arrivals.