Understanding Statistical Averages: Methods and Formulas

[EngWiPy]

Hello,

In some applications, statistical averages are encountered in the derivation of system models. Practically, how can we find the statistical average? Is there mathematical expression to express the expected value?

Thanks in advance

 

[HallsofIvy]

There are several different kinds of "average", or "measure of central tendency" used in statistics.

Given a finite set of numeric data we can use the

mean: Add the numbers divide by how many numbers there are (i.e. the "arthmetic average" you learned in elementary school).

median: Write the numbers in increasing order and pick the "middle number". Relatively easy to find and if the distribution is not symmetric may "measure the central tendency" better than the mean. (Often used for income distributions where there is a lowest possible income, 0, but no highest possible income.)

mode: The value that occurs most often. Not very "precise" and there often is more than one value that occur the same number of times but has the advantage that no arithmetic or ordering is required so it can be applied to non-numeric "values". For example, if you were interested in an "average" 'favorite color' you would have to use the mode.

mid-range. Add the smallest and largest values and divide by 2. Fast and dirty!

 

[EngWiPy]

Yes, but what about the expected value, where the average takes place over all possible values, which may extent to infinite? For example, for an exponential random variable.