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In mathematics and statistics, the term arithmetic mean is preferred over simply "mean" because it helps to differentiate between other means such as geometric and harmonic mean. Statistical mean is the most common term for calculating the mean of a statistical distribution.

An arithmetic mean is calculated using the following equation:

The statistical mean has a wide range of applicability in various types of experimentation. This type of calculation eliminates random errors and helps to derive a more accurate result than a result derived from a single experiment.

The statistical mean can also be used to interpret statistical data. Some important properties make statistical mean very useful for measuring central tendency. They are follows:

If numbers have average X, then:

Since Xi - X is the distance from a given number to the average. The numbers to the left of the mean are balanced by the numbers to the right of the mean. The residuals sum to zero only if a number is a statistical mean. A single number X is used as an estimate for the value of numbers, then the statistical mean minimizes the sum of the squares (xi - X)2 of the residuals.

Statistical mean is popular because it includes every item in the data set and it can easily be used with other statistical measurements. However, the major disadvantage in using statistical mean is that it can be affected by extreme values in the data set and therefore be biased.

The statistical mean is widely used not only in the fields of mathematics and statistics, but also in economics, sociology and history. It gives important information about a data set and provides insight into the experiment and nature of the data.

The other terms used to measure central tendency (an average) are median and mode. In a normal distribution the statistical mean is equal to median and mode.

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