Chapter 11.2, Problem 7PPS

(a)

To determine

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

Answer to Problem 7PPS

The graph of Figure 3 shows that the distribution majority is on the left and there is tail on the left so the distribution is negatively skewed.

Explanation of Solution

Given:

The data set for the sophomore year scores is $1327,1663,1708,1583,1406,1563,1637,1521,1282,1752,1628,1453,1368,1681,1506,1843,1472$ and $1560$ .

The data set for the junior years score is $1728,1523,1857,1789,1668,1713,1834,17691655,1432,1885,1955,1569,1704,1833,2093,1608$ and $1753$ .

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 left 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 7PPS

The mean of the first model is 1523, the standard deviation of the model is 151 and the median is 1561.5. The mean of the second model is 1753.7, the standard deviation of the model is 163.6 and the median is 1761.

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 .1523

The standard deviation of the first model is 151.

From above the mean of the second model is 1753.7

The standard deviation of the second model is 163.6.

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 1561.5.

Thus, the median of the second model is 1761.