Question

a student takes ten exams during a semester and receives the following grades: 90, 85, 97, 76, 89, 58, 82, 102, 70, and 67. find the five - number summary used in a boxplot. which boxplot best represents the data? a. b. c. d.

Explanation:

Step1: Sort the data

First, sort the grades in ascending order: \(58,66,70,76,82,85,89,90,97,102\)

Step2: Find the minimum and maximum

The minimum value \(min = 58\), the maximum value \(max=102\)

Step3: Find the median (\(Q_2\))

Since \(n = 10\) (even), the median \(Q_2=\frac{82 + 85}{2}=83.5\)

Step4: Find the first quartile (\(Q_1\))

The first half of the data is \(58,66,70,76,82\). Since \(n_1 = 5\) (odd), \(Q_1 = 70\)

Step5: Find the third quartile (\(Q_3\))

The second half of the data is \(85,89,90,97,102\). Since \(n_2=5\) (odd), \(Q_3 = 90\)

Now, check each box - plot:

• In a box - plot, the left - most whisker is the minimum, the right - most whisker is the maximum, the left - side of the box is \(Q_1\), the middle line of the box is \(Q_2\), and the right - side of the box is \(Q_3\)
• For option a:
• Minimum is around \(58\), \(Q_1\) is around \(70\), \(Q_2\) is around \(83.5\), \(Q_3\) is around \(90\), maximum is around \(102\)

Answer:

a.