1. The following is a set of data from a sample of n=5.
3 1 4 8 6
a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
2. The following set of data is from a sample of n=6.
1 3 6 1 5 13
a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
3. The following set of data is from a sample of n=7.
15 1 12 14 2 1 4
a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
4. The following is a set of data from a sample of n=5.
10 -2 -1 10 6
a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
5. The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of which is expected to be 575 millimeters. Samples of five tires from each grade were selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are shown below. Complete parts (a) through (c) below.
| Grade X |
Grade Y |
| 563 |
574 |
| 571 |
575 |
| 576 |
576 |
| 582 |
580 |
| 587 |
583 |
a. For each of the two grades of tires, compute the mean, median, and standard deviation.
b. Which grade of tire is providing better quality? Explain. Choose the correct answer below.
- i) Grade Y provides better quality because its mean is much smaller.
- ii) Grade Y provides the better quality. While the mean of Grade X is closer to the expected mean, the standard deviation of Grade Y is much smaller. Your answer is correct.
- iii) Grade X provides better quality because its mean is much smaller.
- iv) Grade X provides the better quality. While the mean of Grade Y is closer to the expected mean, the standard deviation of Grade X is much smaller.
c. What would be the effect on your answers in (a) and (b) if the last value for Grade Y were 589 instead of 583? Explain.
6. The data set below contains spending on products ($) during a three-month period by a sample of 15 customers receiving incentives through a mobile loyalty program. Complete parts (a) through (d) below.
| 55.67 |
22.17 |
67.85 |
46.36 |
57.34 |
108.66 |
50.04 |
35.97 |
| 78.73 |
50.23 |
63.69 |
59.85 |
41.04 |
56.24 |
53.08 |
|
a. Compute the mean and median.
b. Compute the variance, standard deviation, range, and coefficient of variation.
c. Are the data skewed If so, how?
d. Based on the results of (a) through (c), what conclusions can be reached concerning spending on products by customers receiving incentives through a mobile loyalty program?
7. Suppose a bank branch, located in a commercial district, is concerned with its service during the noon-to-1 pm lunch period. The waiting times, in minutes, collected from a sample of 15 customers during this hour, are listed below. Complete parts (a) through (d) below.
a. Compute the mean and median.
b. Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain.
Are there any outliers Explain.
c. Are the data skewed If so, how?
d. As a customer walks into the branch office during the lunch hour, he asks the branch manager how long he can expect to wait. The branch manager replies, "Almost certainly less than 5 minutes." On the basis of the results of (a) through (c), evaluate the accuracy of this statement.
8. The following is a set of data for a population with N = 10.
a. Compute the population mean.
b. Compute the population standard deviation.
9. The table below shows the number of one company's stores located in each of 50 regions. Complete parts (a) through? (c) below.
| 68 |
22 |
75 |
55 |
565 |
81 |
67 |
18 |
12 |
308 |
| 130 |
23 |
28 |
190 |
127 |
69 |
58 |
76 |
81 |
32 |
| 100 |
118 |
155 |
81 |
46 |
100 |
30 |
33 |
45 |
40 |
| 159 |
45 |
345 |
135 |
10 |
205 |
59 |
69 |
232 |
22 |
| 65 |
25 |
88 |
407 |
40 |
20 |
142 |
114 |
35 |
101 |
a. Compute the mean, variance, and standard deviation for this population.
b. What percentage of the 50 regions have stores within plus or minus ±1, plus or minus ±2, or plus or minus ±3 standard deviations of the mean?
c. Compare your findings in part (b) with what would be expected on the basis of the empirical rule. Are you surprised at the results in part? (b)
10. The following is a set of data from a sample of n equals n=7.
0 2 17 3 16 6 11
(a) Compute the first quartile (Upper Q1), the third quartile (Upper Q3), and the interquartile range.
(b) List the five-number summary.
(c) Construct a boxplot and describe the shape.