Question

construct a boxplot for the given data. include values of the 5 - number summary in all boxplots. 16) the test scores of 40 students are listed below. construct a boxplot for the data set. 25 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98 a) 25 58 77 81 98 b) 25 57 78 81 98 c) 25 58 72 81 98 d) 25 57 72 81 98

Explanation:

Step1: Find the minimum value

The minimum value of the data - set is 25.

Step2: Find the first quartile ($Q_1$)

There are $n = 40$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{40+1}{4}=10.25$. The 10th value is 57 and the 11th value is 59. So, $Q_1=57+(59 - 57)\times0.25 = 57.5\approx58$.

Step3: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{40 + 1}{2}=20.5$. The 20th value is 72 and the 21st value is 73. So, $Q_2=\frac{72 + 73}{2}=72.5\approx72$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(40+1)}{4}=30.75$. The 30th value is 81 and the 31st value is 81. So, $Q_3=81+(81 - 81)\times0.75 = 81$.

Step5: Find the maximum value

The maximum value of the data - set is 98.

The 5 - number summary is 25 (minimum), 58 ($Q_1$), 72 ($Q_2$), 81 ($Q_3$), 98 (maximum).

Answer:

C. 25 58 72 81 98