the data set represents the total number of people who bought bananas each hour at a grocery store. 1, 1, 5…

Explanation:

Step1: Find the minimum value

The data set is 1, 1, 5, 5, 7, 8, 8, 10, 12. The minimum value is 1.

Step2: Find the first - quartile (Q1)

There are n = 9 data points. The position of Q1 is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, Q1 is the average of the 2nd and 3rd ordered data points. The 2nd value is 1 and the 3rd is 5, so Q1=$\frac{1 + 5}{2}=3$.

Step3: Find the median (Q2)

The position of the median is $\frac{n+1}{2}=\frac{9 + 1}{2}=5$. The 5th ordered data - point is 7, so Q2 = 7.

Step4: Find the third - quartile (Q3)

The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(9+1)}{4}=7.5$. So, Q3 is the average of the 7th and 8th ordered data points. The 7th value is 8 and the 8th is 10, so Q3=$\frac{8 + 10}{2}=9$.

Step5: Find the maximum value

The maximum value in the data set is 12.

A box - plot has a box from Q1 to Q3 with a line at the median. The whiskers extend from the box to the minimum and maximum values. The box should start at 3, end at 9, have a line at 7, and the whiskers should go to 1 and 12.

Answer:

The box - plot that has a box starting at 3, ending at 9, a line inside the box at 7, and whiskers extending to 1 and 12. (Since no specific option identifiers are given, a description of the correct box - plot is provided).