# Statistical mean

What is a statistical mean?
The statistical mean refers to the mean, or mean, used to derive the central tendency of the data in question. It is found by adding all of the data points in a population and then dividing the sum by the number of points. The resulting number is known as the mean or mean.
In mathematics and statistics, the term arithmetic mean is preferred to the simple "mean" because it helps to differentiate between other means such as the geometric and harmonic mean. The statistical mean is the most common expression used to calculate the mean of a statistical distribution.

An arithmetic mean is calculated using the following equation:

A: = \ frac {1} {n} \ sum_ {i = 1} ^ {n} a_i

The statistical mean has wide applicability in various kinds of experiments. 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. Several important properties make the statistical mean very useful for measuring central tendency. They are as follows:

If numbers have an 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 offset by the numbers to the right of the mean. The residuals only add up to zero when a number is a statistical mean. A single number X is used as an estimate of the value of numbers, then the statistical mean minimizes the sum of the squares (xi - X) 2 of the residuals.
The statistical mean is popular because it includes every point in the data set and can easily be used with other statistical measurements. However, the main disadvantage of using the statistical mean is that it can be influenced by extreme values in the data set and is therefore skewed.

The statistical mean is widely used not only in mathematics and statistics, but also in economics, sociology, and history. It gives important information about a dataset and gives insight into the experiment and the 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 the median and mode.

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