Chapter 11.2, Problem 3CYU

(a)

To determine

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

Answer to Problem 3CYU

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

Explanation of Solution

Given:

The data set for the Mrs Johnson’s Class (dollars ) is shown in Table 1

6	14	17	12	38	15
11	12	23	6	14	28
16	13	27	34	25	32
21	24	21	17	16

Table 1

The distribution for the Mr Edmund’s Class in dollars is shown in Table 2

29	38	21	28	24	33
14	19	28	15	30	6
31	23	33	12	38	28
18	34	26	34	24	37

Table 2

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 3CYU

The mean of the first model is 19.22, the standard deviation of the model is 8.56 and the median is 17. The mean of the second model is 26, the standard deviation of the model is 8.63 and the median is 28.

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 19.22.

The standard deviation of the first model is 8.56.

From above the mean of the second model is 26.

The standard deviation of the second model is 8.63.

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 second model is 28.