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 the minimum, maximum, median, Q1, and Q2

• The data set is \(1,1,5,5,7,8,8,10,12\).
• Minimum (\(min\)): \(1\)
• Maximum (\(max\)): \(12\)
• Median (\(Q2\)): Since \(n = 9\) (odd), the median is the \(\frac{n + 1}{2}\) -th value. \(\frac{9+1}{2}=5\) -th value. So \(Q2 = 7\)
• Lower half: \(1,1,5,5\). \(Q1\) (median of lower half): \(\frac{1 + 5}{2}=3\)
• Upper half: \(8,8,10,12\). \(Q3\) (median of upper half): \(\frac{8+10}{2} = 9\)

Step2: Analyze the box - plot components

• The box - plot should have a whisker starting at \(1\), the box starting at \(3\), the line inside the box at \(7\), the box ending at \(9\), and the whisker ending at \(12\)

Answer:

The first box - plot (with whisker from \(1\) to \(12\), box from \(3\) to \(9\) and median line at \(7\))