The mean, median and mode are common measures of central tendency.
Among the most familiar of statistical concepts, the arithmetic mean or mean refers to a number that we obtain by dividing sum of all the observations in a data series by the count of observations. The simple average has one advantage over the other measures of central tendency that it takes into account the entire information of a data set. One major drawback associated with mean is that it is sensitive to extreme values (small or large).
The mean is an important component when you are going to analyze the variability around the central tendency.
The most important regression analysis is also based on the mean values, wherein the regression line fits through the point corresponding to the means of the dependent and the independent variables.
Population Mean:
An arithmetic mean that is computed for a population (denoted by a μ), also an example of a parameter. A given population contains only one mean and that is unique.
\[ μ = \sum_{i=1}^N \mathbf{X}_i / N \]
where N is number of observations
x _{i} is ith observations