1. Consider the following frequency distribution based on a set of sample data:
X 0 1 2 3 4 5
f 10 17 14 9 3 1
a) What is the sample size?
b) What is the relative frequency of X = 2?
c) What type of frequency distribution is this?
d) Generate the set of cumulative frequencies.
e) The value X = 2 occupies what positions in the ordered data set?
2. Using the following data: -60, 10, 10, 20, -75, 5, 0, 10, 20, 0
a) Calculate the mean, mode, and variance
b) Compute the percentage value for the following K values using Chebychef rule 1 - 1/k2: 3/2, 5/2, 1.36, and 16.
3. a) Name measures of spread and variability. Also, discuss the properties of each
measures.
b) Name 4 types of random samples.
4. In a government agency, 40% of the employees take public transportation to work. Also, 55% of the employees are female. It is assumed that these two characteristics are independent. Draw a tree diagram to illustrate and find the probability that an employee picked at random from this population will be:
a) Female and take public transportation to work.
b) Female and not take public transportation to work.
c) Male and take public transportation to work.
5. The minimum start-up cost for a fast food restaurant chain is as follows for several leading franchises, Units are in thousands of dollars.
|
Company
|
Minimum Start-Up Cost
|
|
McDonald's
|
547.0
|
|
Arby's
|
550.0
|
|
Kentucky Fried Chicken
|
80.0
|
|
Dunkin'Donuts
|
160.0
|
|
Baskin-Robbins USA
|
134.0
|
|
Hardee's
|
714.9
|
|
Dairy Queen
|
405.0
|
|
Domino's Pizza
|
83.0
|
a) Calculate the mean minimum start-up cost.
b) Calculate the standard deviation of the minimum start-up costs.
c) Remove the largest and smallest start-up costs from the data. How is the mean affected?
d) If the largest and smallest start-up costs are removed from the data, do you think that the standard deviation will increase or decrease? Calculate the new standard deviation with these two observation omitted and compare to part (b)
6. The percentage of unemployed workers in each of 20 randomly selected cities are as follows:
3.1 4.5 8.2 1.4 6.3 1.8 2.4 8.8 1.9 2.4
5.4 3.8 7.2 3.8 4.6 7.2 2.5 4.8 3.7 4.2
a) Calculate the 20th percentile.
b) Calculate the 40th percentile.
c) Calculate the 65th percentile.
d) Calculate the 85th percentile.
7. Financial planners often recommend international mutual funds to boost the overall performance of an investor's portfolio. The year's performance figures for U.S. stock funds and for international stock funds are as follows, in percentages.
|
Year
|
U.S. Stock Funds
|
International Stock Funds
|
|
1983
|
21.77
|
27.73
|
|
1984
|
-1.20
|
-4.71
|
|
1985
|
28.52
|
44.44
|
|
1986
|
14.53
|
41.40
|
|
1987
|
1.17
|
7.02
|
|
1988
|
15.75
|
17.43
|
|
1989
|
25.09
|
21.98
|
|
1990
|
-6.11
|
-12.07
|
|
1991
|
36.67
|
12.51
|
|
1992
|
9.11
|
-4.48
|
|
1993
|
9.17
|
25.65
|
a) Calculate the mean, median, variance, standard deviation.
b) Using part (a), describe to an investor the differences between the distributions of the performance figures for the two types of stock funds.
8. Form the summarized table, please answer the following questions:
|
Experience
|
Skill
|
Total
|
|
Bookkeeping
|
Reception
|
Word processing
|
|
Less than one year
|
15
|
5
|
30
|
50
|
|
One to three years
|
5
|
10
|
5
|
20
|
|
More than three years
|
5
|
15
|
10
|
30
|
|
Total
|
25
|
30
|
45
|
100
|
One person's file is selected at random. Determine the probability that the selected person will fall into the following categories.
a) Bookkeeping
b) Less than one year of experience.
c) Reception.
d) One to three years of experience.
e) Word processing.
f) More than three years of experience.
g) Assume the selected person has less than one year of experience. What is the probability that his or her skill is bookkeeping?
h) Determine Pr[bookkeeping and less than one year of experience]. Can the multiplication law be used to determine this probability?
i) Use the addition law to determine the probabilities for the following composite events:
1. Bookkeeping or reception 2. Word processing or reception
9. The 12-month performance of selected stock markets in the world, as measured by each country's Dow Jones Equity Market Index ending October 4, 1993, is as follows. Figures are in percentages.
|
Country
|
12-Month Performance
|
|
Australia
|
17.6
|
|
Canada
|
6.5
|
|
Denmark
|
-1.2
|
|
France
|
9.8
|
|
Germany
|
11.3
|
|
Hong Kong
|
36.3
|
|
Japan
|
42.0
|
|
Netherlands
|
8.8
|
|
Singapore
|
60.0
|
|
Spain
|
22.8
|
|
Switzerland
|
15.4
|
|
United Kingdom
|
11.1
|
|
United States
|
13.3
|
Calculate and interpret each of the statistics in parts (a) through (f).
a) Mean
b) Median
c) Mode
d) Standard deviation
e) Second quartile
f) 20th percentile
10. Advertising expenditures constitute one of the important components of the cost of goods sold. From the following data giving the advertising expenditures (in millions of dollars) of 50 companies, approximate the mean, median, and standard deviation of advertising expenditure.
|
Advertising Expenditure
|
Number of companies
|
|
25 and under 35
|
5
|
|
35 and under 45
|
18
|
|
45 and under 55
|
11
|
|
55 and under 65
|
6
|
|
65 and under 75
|
10
|
|
Total
|
50
|
11. The mean GMAT score of 65 applicants who were accepted into the MBA program of Xavier Business School was 520 with a standard deviation of 25. About how many applicants scored between 470 and 570 on the GMAT?
12. Given the following data, compute the following:
|
Age (in years)
|
Frequency
|
|
20 - 24
|
10
|
|
25 - 29
|
19
|
|
30 - 34
|
27
|
|
35 - 39
|
16
|
|
40 - 44
|
10
|
|
45 - 49
|
6
|
|
50 - 54
|
5
|
|
55 - 59
|
3
|
a) Mean
b) Mode
c) Variance
e) First quartile
f) Second quartile
g) 45th percentile
13. The following table has been prepared from a survey of 100 companies in three industries:
|
|
Computer type
|
|
Industry
|
IBM
|
Apple
|
IBM Compatible
|
Total
|
|
Banking
|
25
|
5
|
5
|
35
|
|
Electronics
|
10
|
20
|
10
|
40
|
|
Accounting
|
25
|
0
|
0
|
25
|
|
Total
|
60
|
25
|
15
|
100
|
To determine the primary type of microcomputer used by employees in the companies, suppose one of these 100 surveyed companies is chosen at random, and answer the following questions:
a) Find P(IBM)
b) Find P(IBM or Electronics)
c) Find P(Apple and Banking)
d) Find P(IBM and Apple)