Chapter 11, Problem 10SGR

(a)

To determine

To find: The histogram for the given data set and then describe the shape of the distribution.

Answer to Problem 10SGR

Thegraph is shown in Figure 5 and the data is positively is skewed.

Explanation of Solution

Given:

The data set for the Iditarod winning times are,

  $\left[\begin{array}{l}9.1,9.4,10.3,9.3,9.6,8.7,9.5,9.4,9.2,17.3,15.4,15.5,14.2,12.0,16.6,13.5,13.0,18.1,12.4,11.6,\\ 11.5,11.3,11.3,13.1,11.2,11.6,11.6,9.7\end{array}\right]$

Calculation:

Press STAT and press 1 to select edit for entering the data as shown in Figure 1

  

Figure 1

Enter all the values in the L1 one by on as shown in Figure 2

  

Figure 2

Press 2^nd and Y= to select the stat plot as shown in Figure 3

  

Figure 3

Select the plot number 1 and select the histogram plot as shown in Figure 4

  

Figure 4

Press the Graph to obtain the plot as shown in Figure 5

  

Figure 5

The histogram plot shows that the right of the median are distributed over the wider range than the data to the left. Thus, the data is positively skewed.

(b)

To determine

To find: The centre and the spread of the data using either the mean and standard deviation of the five number summary.

Answer to Problem 10SGR

Thewinning time of the race is the range from 8.7 to 18.1 the median timing is 11.55 and half of the winning time lies in the interval 9.55 to 11.55.

Explanation of Solution

As the distribution is skewed so use the five number summaries to understand the behaviour of the data.

Calculate the five point summary press the stat and select CALC as shown in Figure 6

  

Figure 6

Press the enter button to calculate the statistical value as shown in Figure 7

  

Figure 7

Scroll down to obtain the five point summary as shown in Figure 8

  

Figure 8

Thus, the winning time of the race is the range from 8.7 to 18.1 the median timing is 11.55 and half of the winning time lies in the interval 9.55 to 11.55,