Exercise 1.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table.

Data Value (# cars)

Frequency

Relative Frequency

Cumulative Relative Frequency

Table 2.39

Exercise 2.

Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. 18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77

a. Find the percentile of 37.

b. Find the percentile of 72.

Solution

Exercise 3.

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain.

Solution

Exercise

4.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

10^th percentile = _______

Solution

Exercise 5.

The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40

Identify the median.

Solution

Exercise 6.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

sample mean = = _______

Solution

Exercise 7.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

mode = _______

Solution

Exercise 8.

What word describes a distribution that has two modes?

Solution

Exercise 9.

Describe the shape of this distribution.

Figure 2.18

Solution

Exercise 10.

Describe the relationship between the mode and the median of this distribution.

Figure 2.22

Solution

Exercise 11.

Describe the relationship between the mean and the median of this distribution.

Figure 2.23

Solution

Exercise 12.

The mean and median for the data are the same.

3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7

Is the data perfectly symmetrical? Why or why not?

Solution

Exercise 13.

Which is the greatest, the mean, the mode, or the median of the data set?

11; 11; 12; 12; 12; 12; 13; 15; 17; 22; 22; 22

Solution

Exercise 14.

In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

a. Organize the data in a chart.

b. Find the median, the first quartile, and the third quartile.

c. Find the 65th percentile.

d. Find the 10th percentile.

e. The middle 50% of the conferences last from _______ days to _______ days.

f. Calculate the sample mean of days of engineering conferences.

g. Calculate the sample standard deviation of days of engineering conferences.

h. Find the mode.

Solution

Exercise 15.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally, sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

a. First quartile = _______

b. Second quartile = median = 50th percentile = _______

c. Third quartile = _______

d. Interquartile range (IQR) = _____ - _____ = _____