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Introduction
Today graphics, tables, reasoning, estimation and prediction are playing a very important role in stating the facts in terms of figures.
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.
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.
Mean Deviation
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.
Mean deviation is also known as average deviation.
The mean deviation is generally denoted by M.D.
Merits and Demerits of Mean Deviation
Merits:
1. Mean deviation is easy to calculate. This measure is simple to understand.
2. This can be calculated from any average.
3. It is less affected by extreme observations.
Demerits:
1. This is mathematically incomplete because it ignores negative signs.
2. As it can be calculated from any average, it does not have certainty (i.e., it is not a well defined measure).
3. Its use is very limited in statistical work.
Standard Deviation
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.
The standard deviation is denoted by s (sigma).
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.
Square of the standard deviation is called the variance.
Calculation of Standard Deviation for discrete series
In the discrete series, when deviations are taken from actual mean, the formula is:
Standard Deviation for continuous series
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.
Merits and Demerits of standard deviation
Merits:
s is based on every item of the data.
s takes care of both positive and negative deviation.
Demerits:
s is some what not easy to understand. The extreme values unduly affect s.
Summary
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.
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.
Conclusion
Statistics is an interesting branch of mathematics which is used in various subjects like politics, history, geography, economics to name a few.
