Question

the test scores of 32 students are listed below. construct a boxplot for the data set
32 37 41 44 46 48 53 55
57 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
81 82 83 86 89 92 95 99
a.
32 56 69.5 80 99
b.
32 56 69.5 79 99
c.
32 56 69.5 80 99

Explanation:

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

• Minimum: The smallest value in the data set is \(32\).
• Maximum: The largest value in the data set is \(99\).
• Median (\(Q2\)): Since \(n = 32\) (even), the median is the average of the \(16^{th}\) and \(17^{th}\) values. The \(16^{th}\) value is \(69\) and the \(17^{th}\) value is \(70\), so \(Q2=\frac{69 + 70}{2}=69.5\).
• First quartile (\(Q1\)): The first half of the data (first \(16\) values). Since \(n_1=16\) (even), \(Q1\) is the average of the \(8^{th}\) and \(9^{th}\) values. The \(8^{th}\) value is \(55\) and the \(9^{th}\) value is \(57\), so \(Q1=\frac{55+57}{2} = 56\).
• Third quartile (\(Q3\)): The second half of the data (last \(16\) values). Since \(n_2 = 16\) (even), \(Q3\) is the average of the \(24^{th}\) and \(25^{th}\) values. The \(24^{th}\) value is \(79\) and the \(25^{th}\) value is \(81\), so \(Q3=\frac{79+81}{2}=80\).

Answer:

A.