ANALYSING DATA TECHNIQUES
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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.
ANALYSING DATA TECHNIQUES
- 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