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# Histograms and polygons

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### Histograms and polygons

1. 1. Stuti Ranjan XI-D
2. 2. “Statistics is the science that deals with the method of collecting, classifying, presenting, comparing ,and interpreting numerical data collected to throw some light on any sphere of enquiry.” -Seligman
3. 3. Collection of data Organisatio n of data Presentation of data Analysis of data Interpretatio n of data Stage 1 Stage 2 Stage 3 Stage 4 Stage 5
4. 4. Each stage of statistical study involves the use of certain techniques or methods Stages Statistical study Statistical tools Stage 1 Collection of data Census or sample method Stage 2 Organisation of data Tally bars Stage 3 Presentation of data Tables, graphs and polygons, histograms etc Stage 4 Analysis of data Percentages ,Averages Stage 5 Interpretation of data Magnitude of percentages
5. 5.  Graphic representation gives a visual effect. Its used in research work for visual presentation and analysis of data. The graphic method enables us to present data in a simple, clear and effective manner  There are many varieties of graphs .Broadly graphs can be divided into two parts: a) Graphs of frequency distribution b) Graphs of time series
6. 6.  Histogram is joining rectangular diagram of a continuous series in which each rectangle represents the class interval with the frequency .It is a two-dimensional diagram and also called frequency histogram. Cases of constructing a hisogram i. Histogram of equal class interval ii. Histogram when mid points are give iii. Histogram when unequal class intervals
7. 7. Scores(mid points) Frequency 5 15 25 35 45 2 5 7 10 4 Ascertainment of lower and upper limits : Get the difference between the first and the second mid point . Divide it by 2 to get the intervals and then draw the histogram.
8. 8. Before presenting the data in the form of graphs and frequencies , unequal class intervals are adjusted. Adjustment factor=class interval of concerned class divided by lowest class interval Marks No of students Adjustment factor Frequency density 30-50 50-60 60-70 70-90 90-100 48 30 20 28 16 20/10=2 10/10=1 10/10=1 20/10=2 10/10=1 48/2=24 30/1=30 20/1=20 28/2=14 16/1=16
9. 9.  Polygon is another form of diagrammatic presentation of data .  It is formed by joining all the mid points of the tops of all rectangles .however they can be formed even without constructing a histogram.  Frequency polygons can be drawn in two ways: i. With a histogram ii. Without a histogram
10. 10. Class limits No of sareees 100-200 200-300 300-400 400-500 500-600 600-700 700-800 10 27 37 24 20 15 10 The total area excluded from the histogram is equal to the area included under frequency polygon
11. 11. Mid points Frequency 55 65 75 85 95 1 4 6 5 2
12. 12. THANK YOU
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