Quantitative Methods in Business Module Lecture (1): Introduction to Quantitative Methods Dr. Mohamed Ramadan moh_ramadan@icloud.com

1. Quantitative Methods
Dr. Mohamed Ramadan
Moh_Ramadan@icloud.com

2. Quantitative Methods
Introduction to
Quantitative Methods
Lecture (1)

3. Lecture (1)
References
Introduction to Quantitative Methods
Key Reference:
Keller, Gerald (2012). Managerial Statistics (9th ed.). South Western, CENGAGE Learning.
Important Readings:
Brett Davies, M. (2007). Doing a Successful Research Project; Using Qualitative or Quantitative Methods.
Palgrave MacMillan.
Cresswell, J (2008). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. Sage
Publications.
Silverman, D (2009). Doing Qualitative Research. Sage Publications.
Keller G. (2010). Managerial Statistics Abbreviated (8th ed.). International Edition, South Western College
Ghauri, P. and Gronhaugh, K. (2005). Research Methods in Business Studies: A Practical Guide. Pearson
Education Ltd.

4. Muhammad Ali
❝I hated every
minute of training,
but I said, Don’t
quit.
Suffer now and
live the rest of
your life as a
champion❞

5. Lecture (1)
Random Variables and Probability Distributions
Introduction to Quantitative Methods
Customers’ Sample
Suppose that you are working in the insurance
department at Pro-Bank ... Your manager asked you
to select a random sample from the VIP
customers, in the age group 40-45 years, whom are
working in company X, which is an about 10
customers. Moreover, he asked you to collect their
Age, Gender and Monthly Salary.
M
42 year
24,500
L.E.
M
40 year
20,000
L.E.
F
40 year
20,000
L.E.
M
41 year
22,000
L.E.
F
42 year
24,500
L.E.
F
42 year
25,000
L.E.
M
40 year
21,000
L.E.
M
43 year
25,000
L.E.
M
44 year
26,000
L.E.
F
41 year
22,000
L.E.
Gender Age (year) Salary (L.E.)
M 42 24,500
M 40 20,000
F 40 20,000
M 41 22,000
F 42 24,500
F 42 25,000
M 40 21,000
M 43 25,000
M 44 26,000
F 41 22,000
Variables

6. Lecture (1)
Random Variables and Probability Distributions
Customers’ Sample
Suppose that you are working in the insurance
department at Pro-Bank ... Your manager asked you
to select a random sample from the VIP
customers, in the age group 40-45 years, whom are
working in company X, which is an about 10
customers. Moreover, he asked you to collect their
Age, Gender and Monthly Salary.
M
42 year
24,500
L.E.
M
40 year
20,000
L.E.
F
40 year
20,000
L.E.
M
41 year
22,000
L.E.
F
42 year
24,500
L.E.
F
42 year
25,000
L.E.
M
40 year
21,000
L.E.
M
43 year
25,000
L.E.
M
44 year
26,000
L.E.
F
41 year
22,000
L.E.
What is a Random Variable?
❝is a function or rule
that assigns a value to
each outcome of an
experiment.❞
Introduction to Quantitative Methods

7. Lecture (1)
Random Variables and Probability Distributions
Customers’ Sample
Suppose that you are working in the insurance
department at Pro-Bank ... Your manager asked you
to select a random sample from the VIP
customers, in the age group 40-45 years, whom are
working in company X, which is an about 10
customers. Moreover, he asked you to collect their
Age, Gender and Monthly Salary.
M
42 year
24,500
L.E.
M
40 year
20,000
L.E.
F
40 year
20,000
L.E.
M
41 year
22,000
L.E.
F
42 year
24,500
L.E.
F
42 year
25,000
L.E.
M
40 year
21,000
L.E.
M
43 year
25,000
L.E.
M
44 year
26,000
L.E.
F
41 year
22,000
L.E.
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Variables Max. Monthly Instalment
= 60% × Salary
Introduction to Quantitative Methods

8. Lecture (1)
Random Variables and Probability Distributions
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Customers’ Sample
Your Manager asked you to brief him with age
distribution?
❝Discrete Random Variable is one that
can take on a countable number of
values.❞
❝Continuous Random Variable is one
which takes an infinite number of
possible values.❞
Introduction to Quantitative Methods

9. Lecture (1)
Random Variables and Probability Distributions
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Customers’ Sample
Your Manager asked you to brief him with age
distribution?
Age
(year)
Frequency Distribution
40 3 3 ÷ 10= 0.3
41 2 2 ÷ 10= 0.2
42 3 3 ÷ 10= 0.3
43 1 1 ÷ 10= 0.1
44 1 1 ÷ 10= 0.1
Sum 10 1.0
0.0 ≤ 𝑃 𝑥 ≤ 1.0
'
!"" #
𝑃 𝑥 = 1.0
𝑥 𝑃 𝑥
Introduction to Quantitative Methods

10. Lecture (1)
Random Variables and Probability Distributions
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Customers’ Sample
Your Manager asked you to brief him with age
distribution?
Age
𝒙
Frequency 𝑃 𝑥
40 3 0.3
41 2 0.2
42 3 0.3
43 1 0.1
44 1 0.1
Sum 10 1.0
Prob. of having customers less than 42
years old? 0.3 + 0.2 = 0.5
50%
Introduction to Quantitative Methods

11. Lecture (1)
Random Variables and Probability Distributions
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Customers’ Sample
Your Manager asked you to brief him with age
distribution?
Age
𝒙
Frequency 𝑃 𝑥
40 3 0.3
41 2 0.2
42 3 0.3
43 1 0.1
44 1 0.1
Sum 10 1.0
Prob. of having customers by max. age of
42 years old? 0.3 + 0.2 + 0.3 = 0.8
80%
Introduction to Quantitative Methods

12. Lecture (1)
Random Variables and Probability Distributions
Gender Age (year) Salary (L.E.) Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
Customers’ Sample
Your Manager asked you to brief him with age
distribution?
Age
𝒙
Frequency 𝑃 𝑥
40 3 0.3
41 2 0.2
42 3 0.3
43 1 0.1
44 1 0.1
Sum 10 1.0
Prob. of having customers not less than 43
years old? 0.1 + 0.1 = 0.2
20%
Introduction to Quantitative Methods

13. Lecture (1)
Discrete Probability Distributions
Customers’ Sample
Your Manager asked you to brief him with Mean
and Variance of Age Distribution?
Age
𝒙
Frequency 𝑃 𝑥
40 3 0.3
41 2 0.2
42 3 0.3
43 1 0.1
44 1 0.1
Sum 10 1.0
𝜇 =
∑$%&
'
𝑥$
𝑁
= '
!"" #
𝑥𝑃 𝑥
𝜎( = '
!"" #
𝑥( 𝑃 𝑥 − 𝜇(
Population Mean:
Population Variance:
Introduction to Quantitative Methods

14. Lecture (1)
Customers’ Sample
Your Manager asked you to brief him with Mean
and Variance of Age Distribution?
Age
𝒙
Frequency 𝑃 𝑥 𝒙𝑃 𝑥 𝒙 𝟐 𝒙 𝟐 𝑃 𝑥
40 3 0.3 12 1600 480
41 2 0.2 8.2 1681 336.2
42 3 0.3 12.6 1764 529.2
43 1 0.1 4.3 1849 184.9
44 1 0.1 4.4 1936 193.6
Sum 10 1.0 41.5 8830 1723.9
𝜇 =
∑$%&
'
𝑥$
𝑁
= '
!"" #
𝑥𝑃 𝑥 = 41.5 𝑦𝑒𝑎𝑟𝑠
𝜎( = '
!"" #
𝑥( 𝑃 𝑥 − 𝜇( = 1723.9 − 41.5( = 1.7
Population Mean:
Population Variance:
1 2 3
4
5
Discrete Probability Distributions
Introduction to Quantitative Methods
𝜎 = 𝑠𝑞𝑟𝑡 𝜎( = 𝑠𝑞𝑟𝑡 1.7 = 1.3 𝑦𝑒𝑎𝑟𝑠

15. Lecture (1)
0.0 ≤ 𝑓 𝑥 ≤ 1.0
Increasing no.
of cases to, e.g.,
100 employee
Gender Age
(year)
Salary
(L.E.)
Max. Monthly
Instalment
M 42 24,500 14,700
M 40 20,000 12,000
F 40 20,000 12,000
M 41 22,000 13,200
F 42 24,500 14,700
F 42 25,000 15,000
M 40 21,000 12,600
M 43 25,000 15,000
M 44 26,000 15,600
F 41 22,000 13,200
:
:
Area under the curve =1.0
Continuous Probability Distributions
Customers’ Sample
Your Manager asked you to brief him with
Monthly Salary Distribution?
𝜇 = 23,000 𝐿. 𝐸.
𝜎( = 2,500
𝜎 = 𝑠𝑞𝑟𝑡 𝜎( = 50 𝐿. 𝐸.
𝒙 = 𝑴𝒐𝒏𝒕𝒉𝒍𝒚 𝑺𝒂𝒍𝒂𝒓𝒚
𝒇𝒙
Introduction to Quantitative Methods

16. Lecture (1)
Continuous Probability Distributions
Customers’ Sample
Your Manager asked you to brief him with the
following probabilities?
𝜇 = 23,000
𝜎( = 2,500
𝜎 = 𝑠𝑞𝑟𝑡 𝜎( = 50
Prob. of attracting employees with maximum
salaries of 23,100 L.E.?
𝑥~𝑁 𝜇, 𝜎 ⟹ 𝑧~𝑍(0,1)
𝒙 = 𝑴𝒐𝒏𝒕𝒉𝒍𝒚 𝑺𝒂𝒍𝒂𝒓𝒚
𝒇𝒙
𝑃 𝑥 < 23,100 = 𝑃
𝑥 − 𝜇
𝜎
<
23,100 − 23,000
50
= 𝑃 𝑧 < 2
𝑧 =
𝑥 − 𝜇
𝜎
1
Introduction to Quantitative Methods

17. Lecture (1)
𝒙 = 𝑴𝒐𝒏𝒕𝒉𝒍𝒚 𝑺𝒂𝒍𝒂𝒓𝒚
𝒇𝒙
𝒛
3
𝒇𝒛
2
𝑃 𝑥 < 23,100 = 𝑃 𝑧 < 2 = 0.5 + 0.4772
= 0.98
4
0.5 0.4772
Introduction to Quantitative Methods

18. Lecture (1)
Continuous Probability Distributions
Customers’ Sample
Your Manager asked you to brief him with the
following probabilities?
𝜇 = 23,000
𝜎( = 2,500
𝜎 = 𝑠𝑞𝑟𝑡 𝜎( = 50
Prob. of attracting employees with maximum
salaries of 22,950 L.E.?
𝑥~𝑁 𝜇, 𝜎 ⟹ 𝑧~𝑍(0,1)
𝒙 = 𝑴𝒐𝒏𝒕𝒉𝒍𝒚 𝑺𝒂𝒍𝒂𝒓𝒚
𝒇𝒙
𝑃 𝑥 < 22,950 = 𝑃
𝑥 − 𝜇
𝜎
<
22,950 − 23,000
50
= 𝑃 𝑧 < −1
𝑧 =
𝑥 − 𝜇
𝜎
1
Introduction to Quantitative Methods

19. 𝒙 = 𝑴𝒐𝒏𝒕𝒉𝒍𝒚 𝑺𝒂𝒍𝒂𝒓𝒚
Lecture (1)
𝒇𝒙
𝒛
𝒇𝒛
2
3
0.5
0.3413
0.5 - 0.3413= 0.1587
4
Introduction to Quantitative Methods

20. Lecture (1)
𝒛
𝒇𝒛
2
3
0.5 - 0.3413= 0.1587
4
𝑃 𝑥 < 22,950 = 𝑃 𝑧 < −1 = 0.5 − 0.3413
= 0.1587 ≅ 0.16
5
0.5
0.3413
Introduction to Quantitative Methods

21. Frank Sinatra
❝Wake up
to reality❞