A probability distribution represents the possible values of a variable and the probability of occurrence of those values. Arithmetic mean and geometric mean of a probability distribution are used to calculate average value of the variable in the distribution. As a rule of thumb, geometric mean provides more accurate value for calculating average of an exponentially increasing/decreasing distribution while arithmetic mean is useful for linear growth/decay functions. Follow a simple procedure to calculate an arithmetic mean on a probability distribution.

Write down the variable and the probability of the variable to occur in the form of a table. For example, the number of shirts sold by a store can be described by the following table where "x" represents the number of shirts sold every day and "P(x)" represents the probability of each event. x P(x) 150 0.2 280 0.05 310 0.35 120 0.30 100 0.10

Multiply each value of x with the corresponding P(x) and store the values in a new column. For example: x P(x) x*P(x) 150 0.2 30 280 0.05 14 310 0.35 108.5 120 0.30 36 100 0.10 10

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Add the result from all the rows of the third column in the table. In this example, arithmetic mean = 30+14+108.5+36+10 = 198.5.

For the example, arithmetic mean gives an average value for the total number of shirts sold on daily basis.

#### Warning

Generally, the term "mean" refers to "arithmetic mean." So use the calculations for arithmetic mean unless specifically asked to do otherwise.