Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

$\begin{array}{c}\text{Average}=\frac{\left\{24\times \text{Average score}+1\times \text{Score}\right\}}{\text{Total students in the class}}\\ =\frac{\left\{24\times 74+1\times 64\right\}}{\left(24+1\right)}\\ =\frac{1,840}{25}\\ =73.6\end{array}$

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.