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Introduction |
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Today graphics, tables, reasoning, estimation and prediction are playing a very important role in stating the facts in terms of figures. |
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Statistics deals mainly in communicating facts and figures in terms of a method called statistical method. Collection, classification, tabulation, representation, reasoning, testing and drawing inferences are part of statistical methods. |
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The word statistics is used with two meanings.
1. Systematically collected and presented numerical data.
2. Processing the numerical data and to draw conclusions from there. |
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Mean Deviation |
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The mean deviation of a statistical data is defined as the arithmetic mean of the numerical values of the deviations of items from some average value. |
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Mean deviation is also known as average deviation. |
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The mean deviation is generally denoted by M.D. |
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Merits and Demerits of Mean Deviation |
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Merits: |
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1. Mean deviation is easy to calculate. This measure is simple to
understand. |
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2. This can be calculated from any average. |
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3. It is less affected by extreme observations. |
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Demerits: |
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1. This is mathematically incomplete because it ignores negative signs. |
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2. As it can be calculated from any average, it does not have certainty (i.e., it is not a well defined measure). |
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3. Its use is very limited in statistical work. |
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Standard Deviation |
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Standard Deviation of a statistical data is defined as the positive square root of the arithmetic mean of the squared deviations of items from their arithmetic mean of the series under consideration. |
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The standard deviation is denoted by s (sigma). |
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The standard deviation is also known as “Root Mean Square Deviation” because it is the square root of the arithmetic mean of the squares of the deviation. |
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Square of the standard deviation is called the variance. |
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Calculation of Standard Deviation for discrete series |
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In the discrete series, when deviations are taken from actual mean, the formula is:
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Standard Deviation for continuous series |
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In this series too deviations may be taken either from the actual mean or from standard mean. The calculations will be simplified if the deviation are taken from assumed mean. |
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Merits and Demerits of standard deviation |
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Merits: |
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s is based on every item of the data. |
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s takes care of both positive and negative deviation. |
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Demerits: |
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s is some what not easy to understand. The extreme values unduly affect s. |
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Summary |
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1. The mean deviation (M.D) of a statistical data is defined as the arithmetic mean of the numerical values of the deviations of the items from some average. |
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2. The standard deviation of a statistical data is defined as the positive square root of the A.M of the squared deviations of items from the A.M. of the series under consideration. |
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Conclusion |
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Statistics is an interesting branch of mathematics which is used in various subjects like politics, history, geography, economics to name a few.
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