Chapter 11.2, Problem 4CYU

(a)

To determine

To find: The box and the whisker plot for the given data set.

Answer to Problem 4CYU

The distribution is negatively skewed and the graph is shown in Figure 3

Explanation of Solution

Given:

The data set for the sophomore season are $42,47,43,46,50,47,52,45,53,55,48,39,40,49,47$ and $50$ .

The data set for the junior season is $44,38,46,48,42,41,42,46,43,40,43,43,44,45,39$ and $44$ .

Calculation:

Use the graphing calculator.

Press STAT and select edit option and enter the values of the table as shown in Figure 1

  

Figure 1

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

  

Figure 2

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

  

Figure 3

The figure 3 shows that the majority on the right and there is tail on the left so the distribution is negatively 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 to justify the choice.

Answer to Problem 4CYU

The mean of the first model is 17.6, the standard deviation of the model is 8 and the median is 15. The mean of the second model is 27.7, the standard deviation of the model is 5.48 and the median is 27.5.

Explanation of Solution

Press the Stat and select CLAC option and select 1 VAR stats and press enter as shown in Figure 4

  

Figure 4

Press enter to obtain the values as shown in Figure 5

  

Figure 5

From above the mean of the first model is 17.6.

The standard deviation of the first model is 8.

From above the mean of the second model is 27.7

The standard deviation of the second model is 5.48.

Press the arrow down of the display screen to find the display screen to find the median as shown in Figure 6

  

Figure 6

Thus, the median of the first model is 15.

Thus, the median of the second model is 27.5.