mean vs expectation

mean and expectation both are nouns.

As nouns, expectation is a hyponym of mean; that is, expectation is a word with a more specific, narrower meaning than mean:

mean: an average of n numbers computed by adding some function of the numbers and dividing by some function of n
expectation: the sum of the values of a random variable divided by the number of values

Other hyponyms of mean include expected value, arithmetic mean, first moment, geometric mean, harmonic mean, Winsorized mean, weighted arithmetic mean, weighted average, weighted mean.

mean (noun)	expectation (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n	belief about (or mental picture of) the future
	anticipating with confidence of fulfillment
	the feeling that something is about to happen
	the sum of the values of a random variable divided by the number of values

mean (adjective)	expectation (adjective)
approximating the statistical norm or average or expected value
characterized by malice
having or showing an ignoble lack of honor or morality
marked by poverty befitting a beggar
(used of persons or behavior) characterized by or indicative of lack of generosity
(used of sums of money) so small in amount as to deserve contempt
of no value or worth
very good; of the highest quality

mean (verb)	expectation (verb)
mean or intend to express or convey
have as a logical consequence
denote or connote
have in mind as a purpose
have a specified degree of importance
intend to refer to
destine or designate for a certain purpose