Statistics

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A bar graph is a pictorial representation of data using bars of uniform width with equal spacing between them. The variable is shown on one axis (usually x-axis) and values on the other axis (y-axis).

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Bar graphs are used for discrete data with gaps between bars, while histograms are used for continuous class intervals with no gaps between rectangles. In histograms, the width of bars is significant

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A histogram is a graphical representation of grouped frequency distribution with continuous classes. Its main characteristic is that there are no gaps between consecutive rectangles, making it appear

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When class intervals are equal, the heights (or lengths) of rectangles are directly proportional to the frequencies of the corresponding class intervals. Since all widths are equal, we can draw rectan

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1. Select the class interval with minimum class size 2. Modify rectangle lengths to be proportionate to this minimum class size 3. Use the formula: New length = (Frequency × Minimum class size) / Actu

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A frequency polygon is formed by joining the mid-points of the upper sides of adjacent rectangles in a histogram using line segments. To complete the polygon, we add imaginary class intervals with zer

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Class-mark is the mid-point of a class interval. It is calculated using the formula: Class-mark = (Upper limit + Lower limit) / 2 For example, for class interval 140-150: Class-mark = (150 + 140) / 2

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Adding imaginary class intervals with zero frequency before the first and after the last class ensures that the area under the frequency polygon equals the area of the corresponding histogram. This ma