PART 2.0: ANALYSING DATA TECHNIQUESOutcome 3.0:

Produce information in appropriate format for decision

making in an organisational context

3.1 Using data from a given business scenario, prepare a range of graphs using spreadsheet – line, pie, bar charts and histograms, and draw valid conclusions based on the information derived

Graphic Presentation of a Frequency Distribution

i. HISTOGRAMii. FREQUENCY POLYGONiii. OGIVE

• similar to bar chart but without the gaps between the bars

a) HISTOGRAM

histogra

m

bar chart

Histogram• class boundaries are marked on the

horizontal axis and class frequencies on the vertical axis represented by the heights of the bars.

1 2 3 4 50

5

10

15

20

25

.

.

Class Boundaries

Freq

uen

cy

HistogramExample 1: Discrete Data: Score for correct answer

Score (x) Freq (f) Class Boundaries

1 – 5 3 0.5 - 5.5

6 – 10 4 5.5 - 10.5

11 – 15 7 10.5 - 15.5

16 – 20 2 15.5 - 20.5

21 – 25 5 20.5 - 25.5

26 - 30 3 25.5 - 30.5

HistogramExample 1: Discrete Data: Score for correct answer

Class Boundari

es

No.

of

Stu

den

ts

0.5 - 5.5 5.5 - 10.5 10.5 - 15.5 15.5 - 20.5 20.5 - 25.5 25.5 - 30.50

1

2

3

4

5

6

7

8

Frequency of Score for the Correct Answer

Score for Correct Answer

No

. o

f S

tud

en

ts

• line segments connecting the points formed by the intersection of the class midpoints and the class frequency.

b) FREQUENCY POLYGON

3 8 13 18 23 280

1

2

3

4

5

6

7

8

Frequency Polygon of Scores for the Correct Answer

Score for Correct Answer

No.o

f S

tud

en

ts

Frequency Polygon

Score (x) Mid-point Freq (f)   -2 0

1 – 5 3 36 – 10 8 4

11 – 15 13 716 – 20 18 221 – 25 23 526 - 30 28 3

  33 0

• Add classes with ‘zero frequencies’ at both ends of the distribution to ‘tie down’ the graph to the horizontal scale.

Frequency Polygon

-2 3 8 13 18 23 28 330

1

2

3

4

5

6

7

8

Frequency Polygon of Scores for the Correct Answer

Score for Correct Answer

No.o

f S

tud

en

ts

Frequency Polygon

-4.5 - 0.5

0.5 - 5.5

5.5 - 10.5

10.5 - 15.5

15.5 - 20.5

20.5 - 25.5

25.5 - 30.5

30.5 - 35.5

0

1

2

3

4

5

6

7

8

Frequency of Scores for the Correct Answer

Score for Correct Answer

No.

of

Stu

den

t

c) OGIVE (Cumulative Freq. Polygon)• reports the number and percent of

observations that occur less than the upper class boundary

• must convert the frequency distribution to a cumulative frequency distribution (F)Score

(x)

Upper Class

Boundaries

Freq (f)

F

1 – 5 5.5 3 36 – 10 10.5 4 711 – 15 15.5 7 1416 – 20 20.5 2 1621 – 25 25.5 5 2126 - 30 30.5 3 24

3(3 + 4)(7 + 7)(14 +

2)(16 + 5)(21 + 3)

Score (x)

Freq (f) UCB F Cum.%

  0 0.5 0 0.01 – 5 3 5.5 3 12.56 – 10 4 10.5 7 29.2

11 – 15 7 15.5 14 58.316 – 20 2 20.5 16 66.721 – 25 5 25.5 21 87.526 - 30 3 30.5 24 100.0

Ogive

Ogive

0.5 5.5 10.5 15.5 20.5 25.5 30.50

5

10

15

20

25

30

Ogive of Scores for the Correct Answer

Score of Correct Answer

Cum

ula

tive F

requency

Histogram with percentages

1 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 - 30 0

1

2

3

4

5

6

7

8

0.0

20.0

40.0

60.0

80.0

100.0

120.0

Frequency of the Scores for Correct Answer

Scores for Correct Answer

Fre

qu

en

cy