Question

question 4 1.5 pts here are three boxplots on an unlabeled number line. image of boxplots a, b, c which boxplot has the following five - number summary? • min = 1 • q1 = 5 • q2 = 6.5 • q3 = 9 • max = 11 options: boxplot a, boxplot b, boxplot c

Explanation:

Step1: Analyze the five - number summary

The five - number summary is \( \text{Min}=1\), \(Q_1 = 5\), \(Q_2=6.5\), \(Q_3 = 9\), \( \text{Max}=11\). Let's recall the components of a boxplot: the left - most point is the minimum, the left edge of the box is \(Q_1\), the line inside the box is the median (\(Q_2\)), the right edge of the box is \(Q_3\), and the right - most point is the maximum. Also, we can look at the relative positions of the minimum, \(Q_1\), median, \(Q_3\), and maximum.

First, the minimum value is 1, which is a relatively small value. Let's analyze the spread between the quartiles:

• The inter - quartile range \(IQR=Q_3 - Q_1=9 - 5 = 4\)
• The distance from \(Q_1\) to \(Q_2\) is \(6.5−5 = 1.5\)
• The distance from \(Q_2\) to \(Q_3\) is \(9 - 6.5=2.5\)
• The distance from the minimum to \(Q_1\) is \(5 - 1 = 4\)
• The distance from \(Q_3\) to the maximum is \(11 - 9=2\)

Now let's analyze the boxplots:

• For Boxplot A: The minimum seems to be relatively far from the box, but the left - most point (min) and the left edge of the box (\(Q_1\)) relationship may not match.
• For Boxplot B: The minimum, \(Q_1\), median, \(Q_3\), and maximum relationships do not seem to fit the given five - number summary.
• For Boxplot C: The minimum value (1) is a single point (the dot) on the left. Then the left edge of the box is \(Q_1 = 5\), the median line inside the box is \(Q_2=6.5\), the right edge of the box is \(Q_3 = 9\), and the right - most point is the maximum \(= 11\). The distances between these points match the calculated distances from the five - number summary (the distance from min (1) to \(Q_1(5)\) is 4, from \(Q_1(5)\) to \(Q_2(6.5)\) is 1.5, from \(Q_2(6.5)\) to \(Q_3(9)\) is 2.5, and from \(Q_3(9)\) to max (11) is 2).

Answer:

Boxplot C