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# [SOLVED]What is the difference between mean and expected value.

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#### anand_jha_30

##### Member level 2
What is the difference between mean and expected value. If they are anyhow different is there any example where the value of the two are different.

Arithmetic mean is simple average of numbers not weighted by anything. However in Expected Value, the numbers are weighted by their probability

Suppose the data set is {1,2,2,3,3,3,4,4,5}. Here the mean is 3. One will calculate EV by (1/9)*1+(2/9)*2+(3/9)*3+(2/9)*4+(1/9)*5. Here again answer is 3. Actually when we multiply by weight we get our data back and we essentially do the same thing. So I again ask is there any difference between the two. can you give an example in your support.

Assume you have the following: two, 1's; ten, 2's; and one, 100. The mean is 61 (edit: 9.4), but the most likely number is 2.

There are all sorts of distributions besides the "normal" distribution. Two common ones seen in biological sciences are the geometric (e.g., 1,2,4,8,16...)(See:Geometric mean - Wikipedia, the free encyclopedia) and log-normal (Log-normal distribution - Wikipedia, the free encyclopedia).

The "median" is useful a parameter for evaluating distributions where the arithmetic average is not the most likely.

John

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@jpanhalt . These things I know. I am asking about. What is the difference between mean and expected value. If there is any? Also in your example mean is 9.3

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If you do an experiment, the expected value is given by the average of all the possible values weighted by their probability. The mean instead is the actual mean value you have after N runs. Statistically:

Average --> Expected Value for N --> infinite.

Of course if you calculate the expected value and the mean on a finite set of value the two calculation will give the same result.

Points: 2

### sameerdamir

Points: 2
Statistically, in probability theory, statistical average means expected value.

Expected value for "first moment" is the "mean" and it is still possible to have expected value for "second moment", "third moment", up to the "Nth moment".

Therefore,

Expected value for first moment = mean

Expected value for second moment is not equal to mean

Expected value for third moment is not equal to mean

Expected value for Nth moment is not equal to mean

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Points: 2

### sameerdamir

Points: 2
Dear Guys,

Please, don't generate confusion for a simple question!
Several of the above answers are completely wrong. Some other go out of the subject.
In probability theory (it is obvious that the question is telling about it), mean and expected value are the same thing.
Regards

Z

go to chapter 18 - The expected value.
We are speaking about a sequence generated by multiple independent experiments, so the mean is not the same thing of the expected value.

Phummy

### Phummy

Points: 2
We are speaking about a sequence generated by multiple independent experiments, so the mean is not the same thing of the expected value.

If you calculate the average of a sequence generated by multiple independent experiments, that is called sample mean.
The "expectad value", "statistical average" or simply "mean" of a random variable is related to its distribution, not to an experiment.
Given a composite experiment, the above-mentionned sample mean is itself a random variable. Instead, the mean is a number.
Regards

Z

Hm kinda tricky question.

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