Generally the following types of graphs are used in representing frequency distribution: 1. Histograms 2. Frequency Polygon 3. Frequency Curve 4. Cumulative Frequency Curve or Ogive 5. Bar Diagram 6. Area of Diagram 7. Circle or Pie Diagram 8. Prisms 9. Cartogram and Map Diagrams 10. Pictogram.
Type # 1. Histrogram:
In drawing the histrogram of a given grouped frequency distribution marks off along a horizontal base-line all the class intervals on a suitable scales, with the class interval as bases draws a rectangles with the area proportional to the frequencies of the respective class intervals. For equal class intervals, the heights of rectangles will be proportional to the frequencies.
f the class intervals are not equal, the heights of the rectangles will be proportional of the ratios of the frequencies to the width of the corresponding classes. A diagram with all these rectangles is known as Histograms.
For example- Draw a histogram further following distribution:
Here,
1 cm = 10 marks
1 cm = 1 frequency
Histograms are also useful when the class-intervals are not of the same width. They are appropriate to cases in which the frequency changes rapidly.
Type # 2. Frequency Polygon:
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If the different points are obtained by plotting the central values of the class-intervals as x-co-ordinates and the respective frequencies as the y-co-ordinates, and these points are joined by straight lines taken in order, they form a polygon are known as frequency polygon.
In a frequency polygon the variables or individuals of each class are assumed to be concentrated at the mid-point of the class-interval.
Type # 3. Frequency Curve:
If through the vertices of a frequency polygon a smooth freehand curve is drawn we get the frequency curve. This is done usually when the class-intervals are of small widths.
Type # 4. Cumulative Frequency Curve or the Ogive:
If from a cumulative frequency table, the upper limits of the class taken as x-co-ordinates and the cumulative frequencies as the y, co-ordinates and the points are plotted, then these points when joined by a freehand smooth curve give the cumulative frequency curve or Ogive.
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Types of Frequency Curves:
Following are some most important types of frequency curves, generally obtained in the graphical representations of frequency distributions:
1. Symmetrical curve or bell shaped curve.
2. Moderately asymmetrical or skewed curve.
3. Extremely asymmetrical or J-shaped curve or reverse J-shaped.
4. U-shaped curve.
5. A bimodal frequency curve.
6. A multimodal frequency curve.
1. Symmetrical Curve or Bell Shaped Curve:
If a curve can be folded symmetrically along a vertical line, it is called a symmetrical curve. In this type the class frequencies decrease to zero symmetrically on either side of a central maximum i.e., the observations equidistant from the central maximum have the same frequency.
2. Moderately Asymmetrical or Skewed Curve:
If there is no symmetry in the curve, it is called skew curve. In this type the class frequencies decrease with greater rapidity on one side of the maximum than on the other. In this type curve one tail is always longer than the other. If long tail is to the positive side, it is called positive skew curve, if long tail is to the negative side in which case it is called negative skew curve.
3. Extremely Asymmetrical or J-Shaped Curve:
When the class frequencies run upto a maximum at one end of the range, they form a J-shaped curve.
4. U-shaped Curve:
In this curve the maximum frequency is at the ends of the range and a maximum towards the centre.
5. A Bimodal curve has two maxima.
6. A multimodal curve has more than two maxima.
Type # 5. Bar Diagrams:
When the comparison of simple magnitude of different item is done the bar diagrams are widely used. In bar diagrams equal bases on a horizontal or vertical line are selected and constructed with the length proportional to the given data. The width of bars is an arbitrary factor. The distance between two bars should be taken about one-half of the width of a bar.
Type # 6. Area Diagrams:
When the difference between two quantities to be compared is large, bars would not depict the comparison so clearly. In such types of squares or circle are used.
Type # 7. Circle or Pie Diagrams:
The pie diagram is a circular graph which denotes the total value with its components. When circles are drawn to denote its area equivalent to the figures, they are call to form pie diagrams or ardes diagrams. In case of circles the square roots of magnitudes are proportional to the radii.
Subdivided Pie Diagram:
Subdivided Pie diagrams are used when comparison of the component parts is done with another and the total. The total value is equated to 360° and then the angles corresponding to components parts are evaluated.
Type # 8. Prisms and Cubes:
When the ratio between the two quantities to be compared is very great so that even area diagrams are not suitable, the data can be denoted by spheres, prisms or cubes. Cubes are constructed on sides which are taken in the ratio of cube roots of the given quantities.
Type # 9. Cartograms or Map Diagrams:
Cartograms or map diagrams are most suitable for geographical data. Rainfalls, temperature in various parts of the country are shown with dots, or shades in a particular map.
Type # 10. Pictograms:
When numerical data are denoted by pictures, they give a more attractive representation. Such pictures are known as pictograms.