# What does the term "expected value" mean?

Apr 15, 2018

see below

#### Explanation:

For real life data the mean of the frequency distribution is calculated by the formula

$\overline{x} = \frac{\sum f x}{n}$

for a probability distribution the expected value is the corresponding calculation; the theoretical mean if you like.

For discrete distributions

$\mu = E \left(X\right) = \sum x P \left(X = x\right)$

for continuous distribution

$\mu = E \left(X\right) = {\int}_{a l l x} x f \left(x\right) \mathrm{dx}$

in both cases since the total probability is $1$ we do not need to divide by anything.