Chapter 11.2, Problem 11PPS

(a)

To determine

To find: The box and the whisker plot for the centre and the spread of the data.

Answer to Problem 11PPS

Therequired graph is shown in Figure 3

Explanation of Solution

Given:

Thepoints scored are $18,10,18,21,9,25,13,17,17,12,24,19,20,17,27,21$ .

Calculation:

Press STAT select the edit option and enter the x and y values as shown in Figure 1

  

Figure 1

Press the 2^nd and the y- button and select the option 1 on the On plot 1 as shown in Figure 2

  

Figure 2

Press the graph key and trace the graph as shown in Figure 3

  

Figure 3

(b)

To determine

To find: The box and the whisker plot for the centre and the spread of the data. Also determine the mean and the median of the new data set.

Answer to Problem 11PPS

Thegraph is shown in Figure 6, the mean of the model is 17.9, and medianis 18. For the changed data the graph is shown in Figure 9, the mean is 14 and the median is 17.

Explanation of Solution

Given:

Thescores are 0, 2, 1 and 0 in the first four games.

Calculation:

Press STAT select the CALC option and select 1 Var stats and press enter as shown in Figure 4

  

Figure 4

Press enter on the display screen to obtain the values as shown in Figure 5

  

Figure 5

From above the mean of the model is $\overline{X}=17.9$ .

The standard deviation of the model is 5.22.

Press the graph key and trace the graph as shown in Figure 3

  

Figure 6

The median of the model is 18.

Change the score of the first four games.

Press STAT select the edit option and enter the x and y values as shown in Figure 7

  

Figure 7

Press the 2^nd and the y- button and select the option 1 on the On plot 1 as shown in Figure 2

  

Figure 8

Press the graph key and trace the graph as shown in Figure 9

  

Figure 9

Press STAT select the CALC option and select 1 Var stats and press enter as shown in Figure 10

  

Figure 10

Press enter on the display screen to obtain the values as shown in Figure 5

  

Figure 11

From above the mean of the model is $\overline{X}=14$ .

The standard deviation of the model is 9.18.

Press the graph key and trace the graph as shown in Figure 12

  

Figure 12

(c)

To determine

To find: The effect that the adding scores from the first four games have on the shape of the distribution and on how you should describe the centre of the spread.

Answer to Problem 11PPS

Theadding of the first four games changes the shape of the distribution as symmetric to being negatively skewed and the median of the two data changes.

Explanation of Solution

Consider that by adding the first four games the shape of the distribution is symmetric to being negatively skewed and the median of the two data changes.