Quantitative Techniques/U6310 Section 2

Fall 2001/Profesor Yang

HANDOUT: WEEK 2 (MEASURES OF CENTRAL TENDENCY AND DISPERSION)

I.          Absenteeism for 50 employees

·               Example of an Ungrouped Frequency Distribution

ABSENTEES

I

II

III

IV

V

Absences

x

Raw Freq.

f

Relative Frequency

 f / N

Cum. Freq.

Cum. Relative Freq

0

3

.06

3

.06

1

2

.04

5

.10

2

5

.10

10

.20

3

8

.16

18

.36

4

7

.14

25

.50

5

2

.04

27

.54

6

13

.26

40

.80

7

2

.04

42

.84

8

4

.08

46

.92

9

0

.00

46

.92

10

1

.02

47

.94

11

2

.04

49

.98

12

0

.00

49

.98

13

1

.02

50

1.00
 

N=50

1.00

    

·              
Example of Histogram using above data

II.             Men’s Heights

·               Example of Grouped Frequency Distribution

Height

Midpt.

Frequency

(f)

Relative Frequency

(f / N)

Percentile

(Cumulative Frequency)

58.5-61.5

60

4

.02

.02

61.5-64.5

63

12

.06

.08

64.5-67.5

66

44

.22

.30

67.5-70.5

69

64

.32

.62

70.5-73.5

72

56

.28

.90

73.5-76.5

75

16

.08

.98

76.5-79.5

78

4

.02

1.00
   

N=200

1.00

  

III.           Measures of Central Tendency (Define, How to Calculate, Pros and Cons, Which measures appropriate for different levels of measurement)

a)     Mode

b)    Media

c)     Mean

IV.           Measaures of Dispersion

a)     Range

b)    Mean Absolute Deviation (MAD)

c)     Variance (Note: difference between population and sample)

d)    Standard deviation (Note: difference between population and sample)

V.             Back to Absenteeism Example: Measures of Dispersion

ABSENTEES

I

II

III

IV

Absences

x

Frequency

f

0

3

-4.86

70.8

1

2

-3.86

29.8

2

5

-2.86

40.9

3

8

-1.86

27.7

4

7

-0.86

5.2

5

2

0.14

.04

6

13

1.14

16.9

7

2

2.14

9.2

8

4

3.14

39.4

9

0

4.14

0

10

1

5.14

26.4

11

2

6.14

75.4

12

0

7.14

0

13

1

8.14

66.3
 

N=50

  

= 408.02