BUSINESS STATISTICS EXERCISES

CHAPTER 2: SUMMARISING DATA
EXERCISE 1:
The table below shows the daily sales (VND 1,000) of internet cafe in Nov/2009 as:

700
940
765
860
870
890
950
650
750
850
855
780
760
735
600
780
920
690
620
730
830
860
750
1000
740
800
750

680
880
790
a. Represent the data using grouped frequency distribution with 4 classes and same class width.
b. Determine the percentage of days with daily sales equal to and more than VND 800,000.
c. Represent the data arranged by appropriate diagram.
EXERCISE 2:
Here are the raw data of total export value (USD million) of 30 enterprises in Hanoi in 2010:

65
45
56
42
57
a. Rearrange the data.

65
57
70
65
69

58
74
40
57
50

77
52

72
52
65

67
80
65
45
66

68
61
78
66
65

b. Represent the arranged data diagrammatically in an appropriate way.
c. Comment on the presentation.

CHAPTER 3: STATISTICAL MEASURES


EXERCISE 1
Here are the sales of bicycles (number of bicycles) over 40 weeks in a shop, as follows:
44

77

40

80

68

44

50

49

56 68

56

48

74

54

78

58

46

79

64 71

62

52

74

63

58

73

64

46

56 69

62

48

66

58

51

70

47

67

52 58

Question:
1. Create the frequency distribution with 4 classes? h=?
2. Determine the average number of bicycles sold in a week; Mode; Me; σ of the number of bicycles
sold?
3. Give a conclusion for the characteristics of this distribution (Moderately Left Skewed?
Moderately Right Skewed? Or Symmetric?)

EXERCISE 2
The table below shows the age of workers in a company:
Age

No of workers
20-24
25-29
30-34
35-39
40-44

973
1122
414
257
258

Age

No of workers
45-49
50-54
55-59
From 60
and over

369
592
825
210

Question:
1. Determine the average age of workers? Standard deviation of age?
2. If you are a HR manager of this company and want to make a policy that reaches the demand of
workers
There are 3 groups of demand after research:
-Group 1: People from ages 20-34: Need for increasing salary
-Group 2: People from ages 35-49: Need for increasing time for relax and
entertainment
-Group 3: People from ages 50 and over: Need for increasing more benefits after
retirement
Which group do you choose to satisfy their demand? Why?


EXERCISE 3

The table below shows the average income of workers in 3 companies, which have produced the
same type of products :
over 12 months of 2009 (Unit: million VND)
A
B
C

3.3
3
2.8

1.8
2
2.1

2
2.1
2

2.1
2.2
2.4

2.4
2.3
2.3

1.8
2
2

2.1
2
2.2

2.2
2.1
2.3

2.4
2.3
2.2

2.3
2.3
2.4

2.4
2.5
2.3

2.8
2.8
2.6

1. Calculate the average monthly income of a worker in each company

2. Determine the median of monthly income of workers in each company
3. Determine the standard deviation of monthly income of workers in every company.
4. Which company should we apply for, if other conditions are similar (mobile

phone support…)?

EXERCISE 4
Determine the average income and variance of income in both groups in a manufacture and give
a conclusion:
Group 1
Income

No of workers

(1000 VND) (people)
1200
1500
2100
2200
2500

3
8
10
6
3

Group 2
Income
(1000
VND)
1500
1800

2100
2200
2500

No of workers
(People)
6
11
7
4
2

EXERCISE 5
The average weight of students in a class is 55 kg with the standard deviation as 6kg.
The average height of students is 165 cm with the standard deviation as 8 cm
Students in the class are similar in term of weight or height?


EXERCISE 6
Research on the average price and standard deviation of price of 2 types of stocks over a period.
Comment on the variability/ dispersion of those two stocks.

Type

Average
(vnd/share)

Price Standard
(vnd/share)

A

20000

4000

B

300000

40000

Deviation

EXERCISE 7
Find the weekly stock price of Wal-Mart for the last six months (go to )
You can ask for the six-month chart and export to a spreadsheet.
1. Calculate the mean and the standard deviation of the stock prices.
2. Get the corresponding data for Tesco and calculate the mean and the standard deviation.
3. The coefficient of variation (CV) is defined as the ratio of the standard deviation over the mean.
Calculate the CV of Wal-Mart and Tesco stock prices.
4. If the CV of the weekly stock prices is taken as an indicator of risk of the stock, how do WalMart and Tesco stock compare in term of risk?
5. Get the corresponding data of the Dow Jones Industrial Average (DJIA) and compute its CV.
How do Wal-Mart and Tesco stocks compare with the DJIA in term of risk?
CHAPTER 4: REGRESSION AND CORRELATION ANALYSIS
EXERCISE 1
Here is an estimated multiple regression model:
Yx1x2x3 = b0 + b1x1 + b2x2 + b3x3

Where:
-

Y: number of products sold in the month (1000 units)
X1: number of people in the area (1000 people)
X2: unemployment rate of the area (%)
X3: expenditure of advertisement (million VND)

Question:
a. Determine the population multiple regression model to find out b0, b1, b2, b3
b. Assume that we have already determine:
b0 = -3.4 , b1 = 0.52, b2 = 0.66, b3 = 0.33
Determine the status of those figures and their meaning.
c. Based on the result found out in b, forecast the sales of that product in the area, whereas the
number of people is 25,650 people; the unemployment rate is 5%; and the expenditure of
advertisement is 30.5 million VND.
EXERCISE 2
American Express Company has long believed that its cardholders tend to travel more extensively
than others – both on business and for pleasure. As part of a comprehensive research effort
undertaken by a New York market research firm on behalf of American Express, a study was
conducted to determine the relationship between travel and charges on the American Express card.
The research firm selected a random of 25 cardholders from the American Express computer file
and recorded their total charges over a specified period. The data are as follow:
Travel
miles

Charges Travel
(USD)
miles

Charges Travel
(USD)
miles

Charges Travel
(USD)
miles

Charges Travel
(USD)
miles

Charges
(USD)

1211

1802

2026

2305

2699

3371

3643

5298

4533

6059

1345

2405

2133

3016

2806

3998

3852

4801

4804

6426

1422

2005

2253

3385

3082

3555

4033

5147

5090

6321

1687

2511

2400

3090

3209

4692

4267

5738

5233

7026

1849

2332

2468

3694

3466

4244

4498

6420

5439

6964

CHAPTER V: TIME SERIES ANALYSIS
EXERCISE 1
A firm’s sales for a product line during the 12 quarters of the past three years were as follows:

YEAR

QUARTER

SALES
(1000 USD)

1

1

2

YEAR

QUARTER

SALES (1000
USD)

600

3

2600

2

1550

4

2900

3

1500

1

3800

4

1500

2

4500

1

2400

3

4000

2

3100

4

4900

3

Estimate a trend line and forecast each quarter of the fourth year using least square method and fourquarter moving average method.

EXERCISE 2
Calculate the trend value using moving average method with three and nine-week period, as followed:
WEEK

ACTUAL WEEK
DEMAND

ACTUAL WEEK
DEMAND

ACTUAL
DEMAND

1

800

11

1700

21

2400

2

1400

12

1500

22

2600

3

1000

13

2300

23

2000

4

1500

14

2300

24

2500

5

1500

15

2000

25

2600

6

1300

16

1700

26

2200

7

1800

17

1800

27

2200

8

1700

18

2200

28

2500

9

1300

19

1900

29

2400

10

1700

20

2400

30

2100


EXERCISE 3
Zeus Computer Chips, Inc., used to have major contracts to produce the Pentium-type chips. The
market has been declining during the past three years because of the dual-core chips, which it cannot
produce, so Zeus has the unpleasant task of forecasting next year. The task is unpleasant because the
firm has not been able to find replacement chips for its product lines. Here is demand over the past 12
quarters:

2005

Actual
demand

2006

Actual
demand

2007

Actual
demand

I

4800

I

3500

I

3200

II

3500

II

2700

II

2100

III

4300

III

3500

III

2700

IV

3000

IV

2400

IV

1700

1. Forecast the four quarters of 2008 using least square method to estimate the trend line?

(Technique for calculating seasonal variation is Additive model).
2. Forecast the four quarters of 2008 using four-quarter moving average to extract the trend?