Chapter 2.1, Problem 19E

(a)

To determine

To find: the mean and median of the measurements.

Answer to Problem 19E

The new mean is 87.188 and the new median is 87.5.

Explanation of Solution

Given:

  

Calculation:

The new mean and the new median both increase by 18 and is obtained below.

  $\begin{array}{l}\text{Mean(new) = }\frac{\text{Sum of student heights standing on chairs}}{\text{number of students}}\\ =\frac{\left(\text{height of first student +18}\right)+\mathrm{...}+\left(\text{height of last student +18}\right)}{\text{number of students}}\\ =\frac{\text{Sum of student heights standing on floor+18}\times \text{number of students}}{\text{number of students}}\\ =\text{Mean}\left(\text{old}\right)+18\\ =69.188+18\\ =87.188\end{array}$

  $\begin{array}{l}\text{Median}\left(\text{new}\right)=\text{Median}\left(\text{old}\right)+18\\ =69.5+18\\ =87.5\end{array}$

The new mean is 87.188 and the new median is 87.5.

Conclusion:

Therefore, the new mean is 87.188 and the new median is 87.5.

(b)

To determine

To find: the standard deviation and IQR of the measurements.

Answer to Problem 19E

The deviations did not change and the IQR, $Q_1$ and $Q_3$ , both increase by 18

Explanation of Solution

For the standard deviation, while the mean increased by 18, the observations each increased by 18 as well so that the deviations did not change. For the IQR, $Q_1$ and $Q_3$ , both increase by 18 so that their difference remains the same as in the original data set.