Diagrammatic and Graphical Representation of Data in Statistics

Diagrammatic representation of Data

1. Diagrammatic Representation of Data

2. One – Dimensional Two – Dimensional Three – Dimensional Pictogram Cartogram Line and Bar Rectangle, Square, Pie Cube, Sphere, etc. Types of Diagrams

3. The length of the lines or bars is considered The width is not considered. Distance between line or bar is kept uniform . Bar – Thick Width Line ONE – DIMENSIONAL DIAGRAM

4. LINE DIAGRAM

5. It is a one –dimensional diagram Easy to understand and common in business. Simple Bar Diagram Year Profits 2012 15000 2013 18000 2014 20000 2015 16000 2016 13000 2017 17000 2018 25000

6. Simple Bar Diagram (Vertical)

7. Simple Bar Diagram (Horizontal)

8. Denote more than one variable Bars are drawn side by side Comparison is easy Multiple Bar Diagram ( Compound)   Profits Year A B 2016 10000 15000 2017 15000 17500 2018 21000 19500

9. Multiple Bar Diagram (Compound)

10. Bar is Subdivided into components . Each Component occupies a part in the bar proportional to its share in the total . To distinguish each component – different colours SUB – DIVIDED BAR DIAGRAM (COMPONENT BAR DIAGRAM)   Districts Population A B C Male 1000 1200 1300 Female 500 800 900 Total 1500 2000 2200

11. SUB – DIVIDED BAR DIAGRAM

12. Bars are all of equal height Each segment (component) shows percentage to the total. Percentage Subdivided Bar Diagram   Districts Population A B C Male 1000 1200 1300 Female 500 800 900 Total 1500 2000 2200 Percentage of Male 1000/1500 *100 = 66.67% 60 59.09 Percentage of Female 500/1500 *100=33.33% 40 40.91

13. Percentage Subdivided Bar Diagram

14. Deviation Bars: depicts the net deviations values both positive and negative Positive values above the base line and negative values below Broken Bars : data contain wide variations( very small or very large) – reasonable shape – larger bars are broken at top Value of each bar written at top. Other Bar Diagrams

15. BROKEN BARS

16. DEVIATION BARS

17. Also called AREA diagram or SURFACE diagram Both length and width is considered Types : Rectangles, Squares, Circles, Pie Diagram . TWO- DIMENSIONAL DIAGRAMS

18. Highly Understandable Proportionate sectors are divided in a circle by taking whole data equal to 360 degrees. PIE DIAGRAM

19. Items Expenditure Angle of the circle Food 87 (87/180)*360 = 174 Clothing 24 48 Entertainment 11 22 Education 13 26 Rent 25 50 Miscellaneous 20 40 Total 180 360 PIE DIAGRAM

20. PIE DIAGRAM

21. Length, Height, Width.. Cubes, Cylinders, Prisms, Spheres… Three Dimensional Diagrams

22. Use of Pictures Use of Maps PICTOGRAMS & CARTOGRAMS

23. 1. They are attractive and impressive . 2. They make data simple and intelligible. 3 . They make comparison possible 4 . They save time and labour. 5 . They have universal utility. 6 . They give more information. 7 . They have a great memorizing effect. Significance of Diagrams and Graphs:

24. DIAGRAMS vs GRAPHS DIAGRAMS GRAPHS Ordinary paper can be used It is attractive and is easily understandable. It is appropriate and effective to represent one or more variables It cannot be used for interpolation and extrapolation technique Median and mode cannot be estimated It is used for comparison only Data are presented by bars, rectangles Diagrams are used for publicity as they are attractive. They give only approximate information. To a statistician or a researcher, diagrams are not helpful in analysis Graph paper is needed It needs some effort to understand It creates problem It is helpful in intrapolation and extrapolation techniques. The value of median and mode can be estimated It represents a mathematical relationship between the two variables. Data are presented by points or lines of different kinds – dots, dashes, etc . Graphs are very much useful to statistician or researchers in analysis.

25. A diagram should be neatly drawn and attractive . The measurements of geometrical figures used in diagram should be accurate and proportional . The size of the diagrams should match the size of the paper. Every diagram must have a suitable but short heading . The scale should be mentioned in the diagram. Diagrams should be neatly as well as accurately drawn with the help of drawing instruments. Index must be given for identification so that the reader can easily make out the meaning of the diagram. Footnote must be given at the bottom of the diagram. Economy in cost and energy should be exercised in drawing diagram RULES for CONSTRUCTING

26. GRAPHICAL REPRESENTATION FREQUENCY DISTRIBUTION

27. TYPES HISTOGRAM FREQUENCY POLYGON FREQUENCY CURVE OGIVES

28. HISTOGRAM FREQUENCY POLYGON & CURVE