Question

which box - and - whisker plot represents this data: 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30?

Explanation:

Step1: Find the minimum, maximum, median, Q1, Q3

The data set is \(6,9,13,13,18,20,22,25,26,28,30,30\).

• Minimum: \(6\)
• Maximum: \(30\)
• Number of data points \(n = 12\) (even). Median \(M=\frac{x_{6}+x_{7}}{2}=\frac{20 + 22}{2}=21\)
• Lower half: \(6,9,13,13,18,20\). \(Q1=\frac{13+13}{2}=13\)
• Upper half: \(22,25,26,28,30,30\). \(Q3=\frac{26+28}{2}=27\)

Step2: Analyze each box - and - whisker plot

• The first plot: Check the positions of \(6\) (minimum), \(13\) (\(Q1\)), \(21\) (median), \(27\) (\(Q3\)), \(30\) (maximum). The box should start at \(13\), end at \(27\), the line inside the box at \(21\), whiskers from \(6\) to \(30\).

Answer:

The first box - and - whisker plot (the one with the box starting around \(13\), median around \(21\), box ending around \(27\), and whiskers from \(6\) to \(30\))