Question

the data set represents the total number of people who bought bananas each hour at a grocery store. 1, 1, 5, 5, 7, 8, 8, 10, 12 which box plot correctly represents the data?

Explanation:

Step1: Find Minimum and Maximum

The data set is \(1, 1, 5, 5, 7, 8, 8, 10, 12\). The minimum value (\( \text{min} \)) is \(1\), and the maximum value (\( \text{max} \)) is \(12\).

Step2: Find Median (Q2)

The number of data points \(n = 9\) (odd). The median is the middle value (5th term). Sorting the data (already sorted), the 5th term is \(7\). So \( \text{Q2} = 7 \).

Step3: Find Q1 (Median of Lower Half)

The lower half of the data (excluding the median) is \(1, 1, 5, 5\). The number of values is \(4\) (even). The median of this subset is the average of the 2nd and 3rd terms: \( \frac{1 + 5}{2} = 3 \). So \( \text{Q1} = 3 \).

Step4: Find Q3 (Median of Upper Half)

The upper half of the data (excluding the median) is \(8, 8, 10, 12\). The number of values is \(4\) (even). The median of this subset is the average of the 2nd and 3rd terms: \( \frac{8 + 10}{2} = 9 \). So \( \text{Q3} = 9 \).

Now, a box - plot has:

• Minimum: \(1\)
• Q1: \(3\)
• Median (Q2): \(7\)
• Q3: \(9\)
• Maximum: \(12\)

We need to check which box - plot has these values for the five - number summary. The box spans from Q1 (\(3\)) to Q3 (\(9\)), with a line at the median (\(7\)), and whiskers from min (\(1\)) to max (\(12\)).

Answer:

To determine the correct box - plot, we analyze the five - number summary (min = 1, Q1 = 3, median = 7, Q3 = 9, max = 12). The box - plot with a box from 3 to 9, a median line at 7, and whiskers from 1 to 12 is the correct one. (Since the specific box - plot options are not fully described in text but the process to identify is based on the five - number summary calculated above)