Question

which box-and-whisker plot represents the data set? 10, 5, 8, 14, 21, 7, 13, 17, 17

Explanation:

Step1: Order the data set

First, we need to order the data set from least to greatest. The data set is \(10, 5, 8, 14, 21, 7, 13, 17, 17\). After ordering, we get: \(5, 7, 8, 10, 13, 14, 17, 17, 21\).

Step2: Find the minimum, maximum, median, Q1, and Q3

• Minimum: The smallest value, which is \(5\).
• Maximum: The largest value, which is \(21\).
• Median: The middle value of the ordered data set. Since there are \(9\) values (an odd number), the median is the \(\frac{9 + 1}{2}=5^{\text{th}}\) value. Looking at the ordered data, the \(5^{\text{th}}\) value is \(13\).
• Q1 (First Quartile): The median of the lower half of the data. The lower half is \(5, 7, 8, 10\) (the values before the median). Since there are \(4\) values (an even number), the median of this subset is the average of the \(2^{\text{nd}}\) and \(3^{\text{rd}}\) values. So, \(Q1=\frac{7 + 8}{2}=\frac{15}{2} = 7.5\).
• Q3 (Third Quartile): The median of the upper half of the data. The upper half is \(14, 17, 17, 21\) (the values after the median). Since there are \(4\) values (an even number), the median of this subset is the average of the \(2^{\text{nd}}\) and \(3^{\text{rd}}\) values. So, \(Q3=\frac{17 + 17}{2}=17\).

Now, we can use these values (minimum \(= 5\), Q1 \(= 7.5\), median \(= 13\), Q3 \(= 17\), maximum \(= 21\)) to identify the correct box - and - whisker plot. The box - and - whisker plot should have:

• The left whisker extending from \(5\) to \(7.5\) (Q1).
• The box from \(7.5\) (Q1) to \(17\) (Q3) with a line at \(13\) (median).
• The right whisker from \(17\) (Q3) to \(21\) (maximum).

(Note: Since the actual box - and - whisker plots are not shown here, but the process to find the key values for the box - and - whisker plot is as above. If we had the plots, we would match the minimum, Q1, median, Q3, and maximum values to the plot.)

Answer:

To determine the correct box - and - whisker plot, we calculate the five - number summary: minimum \(= 5\), Q1 \(= 7.5\), median \(= 13\), Q3 \(= 17\), maximum \(= 21\). The box - and - whisker plot with these values (left whisker: \(5 - 7.5\), box: \(7.5 - 17\) with median line at \(13\), right whisker: \(17 - 21\)) is the correct one. (If plots were labeled, e.g., Plot A, Plot B, etc., we would match the values to the plot's features.)