Question

the box and whisker chart represents the time (minutes) arizonians spent travelling to work. which of the following statements are correct? a the median time is 30 minutes. b half of the people travel at least 15 minutes. c the quickest travel time is 10 minutes. d most of the people travel at least 15 minutes.

Explanation:

Step1: Recall box - and - whisker plot properties

A box - and - whisker plot shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values. The left - most end of the whisker is the minimum value, the right - most end is the maximum value, the left end of the box is $Q_1$, the line inside the box is the median ($Q_2$), and the right end of the box is $Q_3$.

Step2: Analyze each option

• Option A:

The median is the line inside the box. If we assume the scale (evenly spaced), the median is not 30. Let's assume the left end of the box is at 15 (first quartile), the line inside the box (median) is at 25 (not 30).

• Option B:

Half of the data lies between $Q_1$ and $Q_3$. The first quartile ($Q_1$) is 15. So, half of the people travel between 15 and the third quartile. But “at least 15” means from 15 to the maximum. Half of the data is between 15 and the third quartile, not all the data from 15 to the maximum.

• Option C:

The left - most end of the whisker is the minimum value. If we assume the scale, the minimum value is 5 (not 10).

• Option D:

Since $Q_1 = 15$, 75% of the data (because $Q_1$ represents the 25th percentile) is greater than or equal to 15. So, most of the people (75% > 50%) travel at least 15 minutes.

Answer:

D. Most of the people travel at least 15 minutes.