Chapter 11.2, Problem 1CYU

(a)

To determine

To find: The shape of the distribution by the help of graphing calculator.

Answer to Problem 1CYU

The distribution is negatively skewed.

Explanation of Solution

Given:

The given table for the 24 days and the workout time in minutes is shown in Table 1

23	10	18	24	13	27	19	7	25	30	15	22
10	28	23	16	29	26	26	22	12	23	16	27

Table 1

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 of the data is on the right and there is a 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 1CYU

The mean of the model is 20.46, the standard deviation of the model is $6.7$ and the median is 22.5.

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 model is 20.46.

The standard deviation of the model is $6.7$ .

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 is 22.5.