The mean m

See also: Probability parameters introduction, Mean, standard deviation and the Normal distribution

The mean, also known as the expected value, is given by:

                                        for discrete variables

                                  for continuous variables

The mean is known as the first moment about zero. It can be considered to be the centre of gravity of the distribution. If one was to cut out the probability density function drawn on a piece of card, the mean is the value at which the distribution would balance.

Note that the mean is sometimes also referred to as average, though technically they have a different context (i.e. theoretical distributions versus data statistics).

Example

The mean of the Uniform(1,3) distribution is calculated as follows:

            

The mean has the following properties:

mX+Y = mX + mY

mX-Y = mX - mY

mX*Y = mX* mY

where X and Y are positive, uncorrelated random variables.

Read on: The median

 

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