For a particular company with 1,000 employees, Mike conducted a survey about the average one-way commute times, in minutes, between the employees' home and office. A portion of all employees were selected at random and completed surveys online. The result from Mike's survey of 80 employees is summarized below.

Which of the following box plots could represent Mike's survey data?

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Let's examine the schematics of the correct boxplot.

This boxplot gives us the following one-variable statistics:

• Minimum value: 10
• Q1 (1^st Quartile): 20
• Median: 25
• Q3 (3^rd Quartile): 40
• Maximum value: 55

We can find all of these values in the bar plot.

Since there are 80 employees, we can find the corresponding one-variable stats by looking for the following:

• Minimum value: find the employee that has the lowest commute time
• Maximum value: find the employee that has the highest commute time
• Median value: inspect the 40^th employee by either starting from the lowest commute time or the highest commute time (middle)
• Q1: inspect the 20^th employee from the lowest commute time (quarter up from minimum)
• Q3: inspect the 20^th employee from the highest commute time (quarter down from maximum)

Starting from the minimum value, there are 8 employees with a commute time of 10 minutes and 5 employees with a commute time of 5. The next bar includes 13 employees. Therefore, the 20^th largest commute time must be in the next bracket, 20 minutes. This is our Q1 value.

Similarly, if we start from the maximum value and work our way down, there are 15 total employees included in the 45, 50, and 55 minute commute times. The 40 minute bar includes 9 employees, so the 20^th commute time from the maximum must be in the 40 minute bar. This is our Q3.

To find the median, we use the same approach but must go through 39 employees. We can start from either the minimum or maximum and go towards the middle. Since there are 8+5+13=26 employees in the 10, 15, and 20 minute commute time bars, the median must be in the 25 minute bar since there are 22 employees included.

Technically, the 1^st quartile would be found by taking the average of the 20^th and 21^st commute times. Similarly, the median would be found by taking the average of the 40^th and 41^st commute time. The 3^rd quartile would be found by taking the average of the 60^th and 61^st commute time. Typically, SAT questions will allow estimates. For example, for the given question, the 20^th and 21^st commute times are identical and so are the other pairs.