Chapter 1.3, Problem 92E

(a)

To determine

To make: a boxplot of the test score data.

Answer to Problem 92E

  

Explanation of Solution

Given:

  

Calculation:

The box-plot for test score data of Mrs. Liao’s students on their first statistics test is below:

  

Now to check for outliers, we will calculate IQR and then we wil find out the upper and lower limits:

  $\begin{array}{l}IQR=Q_3-Q_1=93.25-81.5=11.75\\ IQRx1.5=11.75x1.5=17.625\\ Q_3+60=93.25+17.625=110.875\\ Q_1-60=81.5-17.625=63.875\end{array}$

Any value above 110.875 and below 63.875 would be an outlier. In this case 43 and 45 are the outliers.

Conclusion:

“Thus, the box-plot is made for the given data”

(b)

To determine

To find: student’s performance on Mrs. L’s first test

Answer to Problem 92E

The students performed very well.

Explanation of Solution

Majority of students have done well in first statistics test. Only two out of thirty students were not able to score well. Since median score is 87.75 and Q1 is also above 70% marks means maximum students have scores above 70. Only two students who have scored 43 and 45 are below the lower range.

Conclusion:

“Therefore, the students performed very well.”