Final answer:
To choose the correct box plot for the data set of employees' ages at Grind Coffee Shop, we organize the ages, find the five-number summary that includes the median (21.5), the first quartile (Q1 - 17), the third quartile (Q3 - 25), the minimum (16), and the maximum (35), and then select the plot that correctly represents these values.
Step-by-step explanation:
The question deals with the representation of a data set through a box plot. A box plot, also known as a box-and-whisker plot, is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
The first step is to organize the data in ascending order: 16, 16, 16, 17, 17, 19, 19, 20, 21, 21, 22, 22, 23, 23, 25, 28, 32, 35. Now we can find the necessary statistics:
• Median: The middle value, which is the average of 21 and 22 in this case, so it is 21.5.
• Q1: The median of the first half of the data, which is 17.
• Q3: The median of the second half of the data, which is 25.
• Minimum: The smallest number in the set, which is 16.
• Maximum: The largest number in the set, which is 35.
With these statistics, we now select the correct box plot, which will have a median line at 21.5, the edges of the box at 17 (Q1) and 25 (Q3), and whiskers that extend to 16 (minimum) and 35 (maximum). The mention correct option in final answer will be the box plot matching these statistics.