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. boxplot a description b. boxplot b description c. boxplot c description d. boxplot d description please select the best answer from the choices provided

Explanation:

Step1: Sort the data

$58,67,70,76,82,85,89,90,97,102$

Step2: Find the minimum

The minimum value is $58$.

Step3: Find the first - quartile ($Q_1$)

Since $n = 10$, the position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So $Q_1=70+(0.75)\times(76 - 70)=74.5$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 10$ is $\frac{n+1}{2}=5.5$. So $Q_2=\frac{82 + 85}{2}=83.5$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So $Q_3=90+(0.25)\times(97 - 90)=91.75$.

Step6: Find the maximum

The maximum value is $102$.

Step7: Analyze box - plots

Based on the five - number summary ($58,74.5,83.5,91.75,102$), we can match with the box - plot.

Answer:

A. Option a