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Probability and Statistics By Sir Dr. Asghar


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Old 08-03-2009, 02:08 PM
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Smartass What is Histogram and Simple examples of Histogram Charts

or the histograms' usage in digital image processing, see Image histogram and Color histogram.

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An example histogram of the heights of 31 Black Cherry trees.

In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent. The intervals (or bands) should ideally be of the same size [1].
Histograms are used to plot density. The total area of a histogram always equals 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.
The word histogram is derived from the Greek histos 'anything set upright' (as the masts of a ship, the bar of a loom, or the vertical bars of a histogram); and gramma 'drawing, record, writing'. The histogram is one of the seven basic tools of quality control, which also include the Pareto chart, check sheet, control chart, cause-and-effect diagram, flowchart, and scatter diagram. A generalization of the histogram is kernel smoothing techniques. This will construct a very smooth probability density function from the supplied data.




Data by proportion
Interval Width Quantity (Q) Q/total/width
0 5 4180 0.0067
5 5 13687 0.0221
10 5 18618 0.0300
15 5 19634 0.0316
20 5 17981 0.0290
25 5 7190 0.0116
30 5 16369 0.0264
35 5 3212 0.0052
40 5 4122 0.0066
45 15 9200 0.0049
60 30 6461 0.0017
90 60 3435 0.0005


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This histogram differs from the first only in the vertical scale. The height of each bar is the decimal percentage of the total that each category represents, and the total area of all the bars is equal to 1, the decimal equivalent of 100%. The curve displayed is a simple density estimate. This version shows proportions, and is also known as a unit area histogram.

In other words a histogram represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies. They only place the bars together to make it easier to compare data.

See some Useful examples for the hostograms

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Histogram of column

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Compare histograms

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Operating Statistics Histogram

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Histogram with overlay Curve

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