graphical representation 4
- 1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 26
- 2. RECAP • Construction of Graphs ( Histogram, Frequency Polygon and Curve) Problems--------------- 02
- 3. LEARNING OBJECTIVES • After Studying this unit, the students able to know how to present data Graphically using Histogram, Frequency Polygon and Curve, and Pie charts and working out cumulative frequency
- 4. LEARNING OUTCOMES • Students will be able to analyze and interpret with in the Contexts they are written in Diagrams and to present data Graphically using Histogram, Frequency Polygon and Curve, and Pie charts
- 5. SESSION - 26 • Construction of Graphs ( Less than Ogive or Cumulative Frequency) Problems---------------02
- 6. Cumulative Frequencies Curve or Ogives MEANING • Cumulative frequency curve (Ogive) is drawn to represent the cumulative frequency distribution. There are two types of Ogives such as ‘less than Ogive curve’ and ‘more than Ogive curve’. To draw these curves, we have to calculate the ‘less than’ cumulative frequencies and ‘more than’ cumulative frequencies. The following procedure can be followed to draw the ogive curves: • Less than Ogive: Less than cumulative frequency of each class is marked against the corresponding upper limit of the respective class. All the points are joined by a free-hand curve to draw the less than ogive curve.
- 7. CONTD • More than Ogive: More than cumulative frequency of each class is marked against the corresponding lower limit of the respective class. All the points are joined by a free-hand curve to draw the more than ogive curve. • Both the curves can be drawn separately or in the same graph. If both the curves are drawn in the same graph, then the value of abscissa (x-coordinate) in the point of intersection is the median.
- 8. CONTD PROBLEM 01 Draw the less than Ogive curve for the following data:
- 9. CONTD Solution; The less than cumulative frequency of Number of workers are plotted as points against the daily wages (upper-limit). These points are joined to form less than ogive curve.
- 10. CONTD
- 11. CONTD PROBLEM 02 The ages of group of pensioners are given in the table below. Draw the Less than ogive to the following data.
- 12. CONTD SOLUTION; Age No of Pensioners CF 65-70 38 38 70-75 45 83 75-80 24 107 80-85 10 117 85-90 8 125
- 13. CONTD 0 20 40 60 80 100 120 140 70 75 80 85 90 CUMULATIVE FREQUENCIES
- 14. SUMMARY As we already discussed and learnt today on Diagrammatic and Graphical Representation as below • Construction of Graphs ( Less than Ogive or Cumulative Frequency) Problems---------------02
- 15. MCQs 1 . Ogive curve can be occurred for the distribution of: (a) Less than type (b) More than type (c) Both (a) and (b) (d) Neither (a) and (b) 2 . The word ogive is also used for: (a) Frequency polygon (b) Cumulative frequency polygon (c) Frequency curve (d) Histogram
- 16. MCQs 3 . Cumulative frequency polygon can be used for the calculation of: (a) Mean (b) Median (c) Mode (d) Geometric mean 4. The graph of the cumulative frequency distribution is called: (a) Histogram (b) Frequency polygon (c) Pictogram (d) Ogive
- 17. MCQs 5 . In a cumulative frequency polygon, the cumulative frequency of each class is plotted against: (a) Mid-point (b) Lower class boundary (c) Upper class boundary (d) Upper class limit
- 18. CONTD ANSWERS 1. C 2. B 3. B 4. D 5. C
- 19. REFERENCES • S.P. Gupta, Sultan Chand and Sons Publications, 2017 • S. C. Gupta, Himalaya Publishing House, Fundamentals of Statistics, 2018 • R.S.N Pillai and Bagavathi, S.Chand publications, 2010
- 20. THANK YOU