Question

which box - and - whisker plot represents this data: 6, 9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?

Explanation:

Step1: Find the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values

• Minimum: The smallest value in the data set \(6,9,13,13,18,20,24,25,26,28,30,30\) is \(6\).
• Median ($Q_2$): For \(n = 12\) (even number of data points), \(Q_2=\frac{6^{th}\text{ value}+7^{th}\text{ value}}{2}=\frac{20 + 24}{2}=22\).
• First quartile ($Q_1$): The lower half of the data is \(6,9,13,13,18,20\). For \(n = 6\) (even), \(Q_1=\frac{3^{rd}\text{ value}+4^{th}\text{ value}}{2}=\frac{13+13}{2}=13\).
• Third quartile ($Q_3$): The upper half of the data is \(24,25,26,28,30,30\). For \(n = 6\) (even), \(Q_3=\frac{3^{rd}\text{ value}+4^{th}\text{ value}}{2}=\frac{26 + 28}{2}=27\).
• Maximum: The largest value is \(30\).

Step2: Match with the box - and - whisker plot

• The whisker starts at the minimum (\(6\)), the box starts at \(Q_1 = 13\), the line inside the box is at the median (\(22\)), the box ends at \(Q_3=27\), and the whisker ends at the maximum (\(30\)).

Answer:

The box - and - whisker plot with the minimum at \(6\), \(Q_1 = 13\), median \(22\), \(Q_3 = 27\), and maximum \(30\) (the one that is colored in the original image) is the correct representation.