1) The document discusses different types of graphs used to present frequency distributions including histograms, frequency polygons, and ogives. 2) A histogram is similar to a bar chart but without gaps between bars, and it shows class boundaries on the x-axis and class frequencies on the y-axis. 3) A frequency polygon connects points formed by the intersection of class midpoints and frequencies with line segments. It can include classes with zero frequencies to "tie down" the graph.

1. PART 2.0: ANALYSING DATA TECHNIQUES
Outcome 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

2. Graphic Presentation of a Frequency
Distribution
i. HISTOGRAM
ii. FREQUENCY POLYGON
iii. OGIVE

3. a) HISTOGRAM
• similar to bar chart but without the gaps
between the bars

4. Histogram
• class boundaries are marked on the horizontal
axis and class frequencies on the vertical axis
represented by the heights of the bars.
25
20
Frequency
15
.
10
5
0
1 2 3 4 5
Class Boundaries
.

5. Histogram
Example 1: Discrete Data: Score for correct
answer
Class
Score (x) Freq (f)
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

6. Histogram
Example 1: Discrete Data: Score for correct
answer Frequency of Score for the Correct Answer
No. of Students
8
7
No. of Students
6
5
4
3
2
1
0
Class
0.5 - 5.5 5.5 - 10.5 10.5 - 15.5 15.5 - 20.5 20.5 - 25.5 25.5 - 30.5
Score for Correct Answer
Boundaries

7. b) FREQUENCY POLYGON
• line segments connecting the points formed by
the intersection of the class midpoints and the
class frequency.
Frequency Polygon of Scores for the
Correct Answer
8
7
6
No.of Students
5
4
3
2
1
0
3 8 13 18 23 28
Score for Correct Answer

8. Frequency Polygon
• Add classes with ‘zero frequencies’ at both
ends of the distribution to ‘tie down’ the graph
to the horizontal scale.
Score (x) Mid-point Freq (f)
-2 0
1–5 3 3
6 – 10 8 4
11 – 15 13 7
16 – 20 18 2
21 – 25 23 5
26 - 30 28 3
33 0

9. Frequency Polygon
Frequency Polygon of Scores for the Correct
Answer
8
7
6
No.of Students
5
4
3
2
1
0
-2 3 8 13 18 23 28 33
Score for Correct Answer

10. Frequency Polygon
Frequency of Scores for the Correct Answer
8
7
6
No. of Student
5
4
3
2
1
0
-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
Score for Correct Answer

11. 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)
Upper Class
Score (x) Freq (f) F
Boundaries
1–5 5.5 3 3 3
6 – 10 10.5 4 7 (3 + 4)
11 – 15 15.5 7 14 (7 + 7)
16 – 20 20.5 2 16 (14 + 2)
21 – 25 25.5 5 21 (16 + 5)
26 - 30 30.5 3 24 (21 + 3)

12. Ogive
Score (x) Freq (f) UCB F Cum.%
0 0.5 0 0.0
1–5 3 5.5 3 12.5
6 – 10 4 10.5 7 29.2
11 – 15 7 15.5 14 58.3
16 – 20 2 20.5 16 66.7
21 – 25 5 25.5 21 87.5
26 - 30 3 30.5 24 100.0

13. Ogive
Ogive of Scores for the Correct Answer
30
25
Cumulative Frequency
20
15
10
5
0
0.5 5.5 10.5 15.5 20.5 25.5 30.5
Score of Correct Answer

14. Histogram with percentages
Frequency of the Scores for Correct Answer
8 120.0
7
100.0
6
80.0
5
Frequency
4 60.0
3
40.0
2
20.0
1
0 0.0
1–5 6 – 10 11 – 15 16 – 20 21 – 25 26 - 30
Scores for Correct Answer