Chapter 4, Problem 23E

(a)

To determine

To Explain: the spread in running times on the basis of the quartiles and the standard deviation.

Explanation of Solution

Given:

  $\begin{array}{l}\text{standard}\text{deviation}=19.6\text{minutes}\\ Q_1=97\text{minutes}\\ Q_3=119\text{minutes}\end{array}$

Quartile: the middle 50% of runners ran between 97 and 119 minutes, for a 22 minute range. Standard deviation: in general, the centre range of runners ran within 19.6 minutes of each other. These are general definition of quartile and standard deviation.

(b)

To determine

To Explain: the about of spread.

Explanation of Solution

Given:

  $\begin{array}{l}\text{standard}\text{deviation}=19.6\text{minutes}\\ Q_1=97\text{minutes}\\ Q_3=119\text{minutes}\end{array}$

The use of standard deviation might be misleading here. The data is skewed rightward, with few outliers that cause the spread to be a little misrepresented. In general, the spread would be smaller if these items were not here.