Statistics lecture 3 (ch2)

2

• Need to gain information from data.

• Data must be organised and reduced.

• Descriptive statistics

– Organising data into tables, charts and graphs.

– Numerical calculations.

• Single variable data

• Raw data

– Collected data before it is grouped or ranked.

3

Example: The data below shows the gender of 50 employees and the

department in which they work at ABC Ltd.

Organising and graphing qualitative data in a

frequency distribution table.

Emp. no. Gender Dept. Emp. no. Gender Dept …..

1 M HR 6 M Fin. …..

2 F Mark. 7 M Mark. …..

3 M Fin. 8 M Fin. …..

4 F HR 9 F HR …..

5 F Fin. 10 F Fin. …..

M – Male

F – Female

HR – Human resources

Mark. – Marketing

Fin. – Finance

4

Emp. no. Gender Dept. Emp. no. Gender Dept …..

1 M HR 6 M Fin. …..

2 F Mark. 7 M Mark. …..

3 M Fin. 8 M Fin. …..

4 F HR 9 F HR …..

5 F Fin. 10 F Fin. …..

HR Marketing Finance

M

F │

│

│

│ │

│ │

│ │

│

5

HR Marketing Finance

M 4 10 5

F 10 16 5

Organising and graphing qualitative data in a frequency

distribution table.

6

HR Marketing Finance Total

M 4 10 5 19

F 10 16 5 31

Total 14 26 10 50

Organising and graphing qualitative data in a frequency

distribution table.

7

Pie charts

HR Mark Fin Total

Total 14 26 10 50

Degrees 14/50×360

= 101

26/50×360

= 187

10/50×360

= 72 360

Percentage 14/50×100

= 28

26/50×100

= 52

10/50×100

= 20 100

Employees at ABC

28%

52%

20%

Human resources

Marketing

Finance

8

Pie charts

Male Female Total

Total 19 31 50

Degrees 19/50×360

= 137

31/50×360

= 223 360

Percentage 19/50×100

= 38

31/50×100

= 62 100

Employees at ABC

38%

62%

Male

Female

9

Bar graphs

Employees at ABC

14

26

10

0

5

10

15

20

25

30

Human

resources

Marketing Finance

Num

ber

of

work

ers

Employees at ABC

19

31

0

5

10

15

20

25

30

35

Male Female

Num

ber

of

work

ers


M 4 10 5 19

F 10 16 5 31

Total 14 26 10 50

10

Employees at ABC

0

5

10

15

20

Male Female

Num

ber

of w

ork

ers

Human

resources

Marketing

Finance

Employees at ABC

0

5

10

15

20

Human

resources

Marketing Finance

Num

ber

of w

ork

ers

Male

Female

Multiple bar graphs


M 4 10 5 19

F 10 16 5 31

Total 14 26 10 50

11

Employees at ABC

0

5

10

15

20

25

30

35

Male Female

Num

ber

of w

ork

ers

Finance

Marketing

Human

resources

Employees at ABC

05

1015202530

Human

resources

Marketing Finance

Num

ber

of

work

ers

Female

Male

Stacked bar graphs


M 4 10 5 19

F 10 16 5 31

Total 14 26 10 50

Definitions

Frequency Distribution

– for qualitative data displays the possible categories

along with the number of times (or frequency) each

category appears in the data set.

- for quantitative data is a summary of numerical data

prepared by dividing raw data into several non-

overlapping class intervals and then counting how

many observations (frequency) of the variable fall into

each class

Relative Frequency – for a particular category is the

portion or % of the observations within a category 12

13

• Frequency table consists of a number of classes and each observation is counted and recorded as the frequency of the class.

• If n observations need to be classified into a frequency table, determine:

–

– max minClass widthx x

c

Organising and graphing quantitative data in a frequency

distribution table.

Number of classes:

1 3,3logc n

14

Example: The following data represents the number of telephone calls

received for two days at a municipal call centre. The data was

measured per hour.

8 11 12 20 18 10 14 18 16 9

5 7 11 12 15 14 16 9 17 11

6 18 9 15 13 12 11 6 10 8

11 13 22 11 11 14 11 10 9

19 14 17 9 3 3 16 8 2

Organising and graphing quantitative data in a frequency

distribution table.

15

1 3,3log

1 3,3log 48 6,5 7

Number of classes n

max min 22 22,86 3

7

x xClass width

k

Frequency distribution

8 11 12 20 18 10 14 18 16 9

5 7 11 12 15 14 16 9 17 11

6 18 9 15 13 12 11 6 10 8

11 13 22 11 11 14 11 10 9

19 14 17 9 3 3 16 8 2

16

– first class min min[ ; )x x class width[ 2 ; 2 3 )[ 2 ; 5 )

– second class [ 5 ; 5 3 )[ 5 ; 8 )[ 5 ; 5 )class width


8 11 12 20 18 10 14 18 16 9

5 7 11 12 15 14 16 9 17 11

6 18 9 15 13 12 11 6 10 8

11 13 22 11 11 14 11 10 9

19 14 17 9 3 3 16 8 2

“[“ value is included in class

“)“ value is excluded from class

Classes Count

[2;5)

[5;8)

[8;11)

[11;14)

[14;17)

[17;20)

[20;23)

17

3

4

11

13

9

2

6

8 11 12 20 ….

5 7 11 12 ….

6 18 9 15 ….

11 13 22 11 ….

19 14 17 9 ….


|

|

|

|

|

|

│││

││││

│││││││││

│││││││││││││

│││││││││││

││││││

││

18

Classes Frequency (f)

[2;5) 3

[5;8) 4

[8;11) 11

[11;14) 13

[14;17) 9

[17;20) 6

[20;23) 2

Total 48


19

Classes f % frequency

[2;5) 3 3/48×100 = 6,3

[5;8) 4 4/48×100 = 8,3

[8;11) 11 11/48×100 = 22,9

[11;14) 13 27,1

[14;17) 9 18,8

[17;20) 6 12,5

[20;23) 2 4,2

Total 48 100


20

Classes f % f Cumulative frequency (F)

[2;5) 3 6,3 3

[5;8) 4 8,3 3 + 4 = 7

[8;11) 11 22,9 7 + 11 = 18

[11;14) 13 27,1 18 + 13 = 31

[14;17) 9 18,8 31 + 9 = 40

[17;20) 6 12,5 40 + 6 = 46

[20;23) 2 4,2 46 + 2 = 48

Total 48 100


21

Classes f % f F % F

[2;5) 3 6,3 3 3/48×100 = 6,3

[5;8) 4 8,3 7 7/48×100 = 14,6

[8;11) 11 22,9 18 18/48×100 = 37,5

[11;14) 13 27,1 31 64,6

[14;17) 9 18,8 40 83,3

[17;20) 6 12,5 46 95,8

[20;23) 2 4,2 48 100

Total 48 100


22

Classes f F Class mid-points (x)

[2;5) 3 3 (2 + 5)/2 = 3,5

[5;8) 4 7 (5 + 8)/2 = 6,5

[8;11) 11 18 (8 + 11)/2 = 9,5

[11;14) 13 31 (11 + 14)/2 = 12,5

[14;17) 9 40 15,5

[17;20) 6 46 18,5

[20;23) 2 48 21,5

Total 48


23

Classes f % f F % F (x)

[2;5) 3 6,3 3 6,3 3,5

[5;8) 4 8,3 7 14,6 6,5

[8;11) 11 22,9 18 37,5 9,5

[11;14) 13 27,1 31 64,6 12,5

[14;17) 9 18,8 40 83,3 15,5

[17;20) 6 12,5 46 95,8 18,5

[20;23) 2 4,2 48 100 21,5

Total 48 100


24

Classes f % f

[2;5) 3 6,3

[5;8) 4 8,3

[8;11) 11 22,9

[11;14) 13 27,1

[14;17) 9 18,8

[17;20) 6 12,5

[20;23) 2 4,2

y-axis

x-axis

Histograms

25

Histograms

Number of telephone calls per hour

at a municipal call centre

0

2

4

6

8

10

12

14

Number of calls

Nu

mb

er

of

ho

urs

2 5 8 11 14 17 20 23

Definitions

Frequency Polygon

A line graph of a frequency distribution and offers

a useful alternative to a histogram. Frequency

polygon is useful in conveying the shape of the

distribution

Ogive

A graphic representation of the cumulative

frequency distribution. Used for approximating the

number of values less than or equal to a specified

value 26

27

Class mid-points (x) f % f

3,5 3 6,3

6,5 4 8,3

9,5 11 22,9

12,5 13 27,1

15,5 9 18,8

18,5 6 12,5

21,5 2 4,2

y-axis

x-axis

Frequency polygons

28

Number of telephone calls per hour

at a municipal call centre

0

2

4

6

8

10

12

14

0.5 3.5 6.5 9.5 12.5 15.5 18.5 21.5 24.5

Number of calls

Nu

mb

er

of

ho

urs

Arbitrary mid-points to

close the polygon.

(x)

3,5

6,5

9,5

12,5

15,5

18,5

21,5

Frequency polygons

29

Classes F % F

[2;5) 3 6,3

[5;8) 7 14,6

[8;11) 18 37,5

[11;14) 31 64,6

[14;17) 40 83,3

[17;20) 46 95,8

[20;23) 48 100

y-axis

x-axis

Ogives

30

Ogive of number of call received

at a call centre per hour

0102030405060708090

100

2 5 8 11 14 17 20 23

Number of calls

% C

um

ula

tiv

e

nu

mb

er

of

ho

urs

None of the hours had

less than 2 calls.

Ogives

31

Ogive of number of call received

at a call centre per hour

0102030405060708090

100

2 5 8 11 14 17 20 23

Number of calls

% C

um

ula

tiv

e

nu

mb

er

of

ho

urs

Ogives

50% of the hours had less

than 12 calls per hour.

80% of the

hours had

less than

17 calls

per hour.

20% of the

hours had

more than

17 calls

per hour.

32

• Activity 1 Module Manual p 67



• Revision Exercise 1 Module Manual p 70


33



• Concept Questions 1 -11 p 52 Elementary

Statistics

• Self Review Test p53 Elementary Statistics

• Supplementary Exercises p 54 -59

Elementary Statistics

Statistics lecture 3 (ch2)

Education

Transcript of Statistics lecture 3 (ch2)