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Histogram, bar graph,line graph, ogive , frequency polygon,

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- 1. Graphs
- 2. A Graph is Used to show the variations in a variable by means of a curve or a straight. Persons seeing graphs have not to bother themselves about the figures. Utility Of Graphic Presentation (1)Presentation Of Time Series and Frequency Distribution : Graphic Presentation is a very effective technique of data presentation in case of time series and frequency distributions (2)Location of Averages: Using graphic technique, we can easily locate the value of certain averages, such as mode and median. If it is not possible with help of diagram (3)Easy Estimation : Graphic presentation facilitates interpolation and extrapolation of the data in a more convenient and precise manner. For example, given population data for the years 1951 and 1971, one can easily make an estimate of the population in the years 1981 or 1991 (4) Study Of Correlation : Graphic technique helps in studying correlation between different variables, such as price and demand, cost and output. (5) Comparison Of Multiple-Dam: Data of different dimensions can be easily compared with help of graphic presentation.
- 3. Limitations Of Graphic Presentation (1) Less Significant : Graphs are not equal significance to all the people. It is generally difficult for layman to interpret graphs (2) Only a Measure Tendency : Graphs show only tendency of data. Actual values are not always clear from graphs. (3) Lack of precise Value: Since graphs are based on brief information, these do not show precise values. (4) Wrong Conclusion : Graphs may sometimes suggest wrong conclusions. In fact even a small change in the scale of graphs causes a lot of difference in structure of graph. This may lead to wrong conclusions.
- 4. Graphs Time Series Graphs One- variable Two- variable More than two variable Frequency Graphs Frequency Bars Histogram Frequency Polygon Frequency Curve Ogive
- 5. Time Series Graphs • A time series is an arrangement of statistical data in a Chronological order. The Graph of time series with time on X-axis and dependent variable on Y-variable is called a historigrams. • Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data
- 6. Year Amount(`Crore) 1990-91 227 1991-92 127 1992-93 403 1993-94 554 1994-95 379 1995-96 270 1996-97 686 1997-98 581 1998-99 721 One Variable Graphs One variable graphs are those graphs in which values of only one variable are shown with respect to different time periods. This table shows the net revenue earned by railways during nine Years
- 7. 0 100 200 300 400 500 600 700 800 `Crore Years Amount Amount Net revenue for Indian Railways
- 8. Month Jan Feb Mar April May June Production 7.5 10 7.5 12.5 15 17.5 Sale 5 7.5 5 10 12.5 15 0 2 4 6 8 10 12 14 16 18 20 Production/Sale Month Production Sale Two or More than two variable graphs
- 9. Frequency Distribution Graphs are those graphs which present the frequency distribution of data on graph paper. These graphs are prepared to present those data which are not related to any time period. The data presented in these graphs are in the form of frequency distribution,ethier grouped or ungrouped. It quickly Calls attention to high to low points in the distribution.
- 10. A line Frequency Graph is that which presents a discrete frequency distribution of data on graph paper. In such graph, various items of values are shown on X- axis and their corresponding frequencies on Y-axis. Frequency of the values are shown in the Form of vertical straight lines.
- 11. 5 6 10 15 12 5 0 2 4 6 8 10 12 14 16 45 50 55 60 65 70 No.ofStudents Height In Inches Line Frequency Graph Frequency Height(in Inches) 45 50 55 60 65 70 No of Students 5 6 10 15 12 5
- 12. An Histogram Is a Graphical Representation of a frequency of a frequency distribution of a continuous series. It represents the class frequencies in a frequency distribution by vertical rectangles meeting each other from left to right. The Total area covered under a histogram is proportional to the total frequency.
- 13. 3 5 9 15 18 13 11 7 4 0 5 10 15 20 5 10 15 20 25 30 35 40 45 50 Histogram Frequency 5 10 15 20 25 30 35 40 45 50 Class-Interval Frequency Class-Interval Frequency 5-10 3 30-35 13 10-15 5 35-40 11 15-20 9 40-45 7 20-25 15 45-50 4 25-30 18
- 14. When the class intervals are unequal, frequencies are first adjusted before constructing a histogram. For making the adjustment, we first determine the adjustment factor by using the formula: Adjusted Factor=Size of class interval/lowest class interval. Then we divide the frequencies by adjustment factor and obtain the new adjusted frequency density, The height of the rectangles would be proportional to the adjusted frequencies
- 15. Class-Interval Frequency Adjustment Factor Frequency Density 4-8 3 4/4= 1 3/1=3 8-12 9 4/4= 1 9/1=9 12-16 15 4/4= 1 15/1=15 16-20 18 4/4=1 18/1=18 20-28 20 8/4=2 20/2=10 28-40 15 12/4=3 15/3=5 40-56 12 16/4=4 12/4=3
- 16. 3 9 15 18 0 0 2 4 6 8 10 12 14 16 18 20 4 8 12 16 20 24 28 32 36 40 44 48 52 56 Histogram Series 1 5 3 4 8 12 16 20 24 28 32 36 40 44 48 52 56 Markss
- 17. There are two ways in which frequency polygon may be constructed : (a)By histogram (b)Without Histogram A graph of a frequency distribution with values of the variable on the x-axis and the number of observations on the y-axis; data points are plotted at the midpoints of the intervals and are connected with a straight line.
- 18. 0 2 5 4 14 12 5 3 0 2 4 6 8 10 12 14 16 102 113 124 135 146 157 168 179 Histogram with Frequency polygon Histogram 102 113 124 135 146 157 163 179 Weight 102-113 113-124 124-135 135-146 146-157 157-168 168-179 No of men(f) 2 5 4 14 12 5 3
- 19. C.I Wages(`) Class Boundaries No of Workers(frequency) Mid Value 1-10 0.5-10.5 14 5.5 11-20 10.5-20.5 28 15.5 24-30 20.5-30.5 36 25.5 31-40 30.5-40.5 12 35.5 41-50 40.5-50.5 10 45.5
- 20. 0 14 28 36 12 10 0 0 5 10 15 20 25 30 35 40 0.5 5.5 15.5 25.5 35.5 45.5 50.5 NoOfWorkers Frequency Polygon Frequency
- 21. A Frequency Curve is the smoothed form of frequency polygon. A frequency curve is obtained by joining the points of a frequency polygon through free hand smoothed curves and not through straight lines. Area of a frequency curve is equal to the area of a frequency polygon
- 22. 0 5 10 15 20 25 10 5 15 25 35 45 55 60 NoOfStudents Frequency Curve Frequency Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of students 5 12 15 22 14 4 Mid values 5 15 25 35 45 55
- 23. An Ogive is the curve which is constructed by plotting the cumulative frequencies in the form of smooth curve. From such curves, We come to know about the frequencies corresponding to a certain lower or upper limits in the distribution of the data. There are two methods of constructing an Ogive: (A)Less-than Method (B)More-than Method
- 24. Marks No of students 0-10 2 10-20 3 20-30 5 30-40 8 40-50 4 40-60 3 60-70 5 Marks(less than) Cumulative Frequency 10 2 20 2+3=5 30 5+5=10 40 10+8=18 50 18+4=22 60 22+3=25 70 25+2=30 In this method, we start with the upper limits of the classes and go on adding frequencies. When these frequencies are plotted, we get a rising curve. The resultant curve is called “less than Ogive”.
- 25. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 No.ofStudents Marks Less than Ogive Frequency
- 26. Marks No of students 0-10 2 10-20 3 20-30 5 30-40 8 40-50 4 50-60 3 60-70 5 Marks(more than) Cumulative Frequency 0 28+2=30 10 25+3=28 20 20+5=25 30 12+8=20 40 8+4=12 50 5+3=8 60 5 In this method, we start with the lower limits of the classes and add frequencies from the bottom. When the frequencies are plotted, we get a declining curve. The resultant curve is called a “More than Ogive”
- 27. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 60 70 No.ofStudents Marks More than Ogive Frequency

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