Understanding Expected Value vs Average | Explained by Michael

We delve into the difference between an expected value and the average, looking at a case where they are the same and cases where they differ.

This is the 2nd video in a series on understanding topics conceptually in probability and statistics. When we understand the root level, formulas often no longer are worrisome and difficult.

[BonnieX]

I am an Economics and Statistics major, doing pretty well these days in academics but it probably took me a year for a concept of Expected value to be fully internalized.


Good explanation. Keep up the good work, I am sure, views will come.

[rhinobridge]

In conclusion: the expected value corresponds to the arithmetic mean when all probabilities are the same and corresponds to the weighted mean when probabilities differ.

[zio.eza]

finally, I can understand this intuitively. I'm non-native speaker but I can understand him completely. Thank you sir!

[isurikariyawasam]

Your explanation was so good, I didn't even need to watch the whole video, it finally clicked! Thank you!

[thehyperfinestructure]

I'm learning Statistics for Data Science and this video helped me learn the difference between these two concepts!
Keep up the good work!

[connorwadwell]

Thanks heaps! You explained in such an intuitive and simple way, its much easier than I originally thought!

[HpeAnLve]

i appreciate the time you took making this, good work.

[roshanpandey]

You are doing a great job. Keep up the good work...

[seeker]

Just wanted to say you are awesome and Thank you for the clear and well explained video.

[shahramsohail]

You are unecessarily complicating it.
Expected value is used when we want to calculate the mean of a probability distribution. This represents the average value we expect to occur before collecting any data.
Mean is typically used when we want to calculate the average value of a given sample. This represents the average value of raw data that we’ve already collected.
That's it...

[science_engineering]

Only me noticed that this guy is almost like Sheldon Cooper?🤣
He's talking like him, his back and hair are looking exactly the same like Sheldon's ones😁

[elbertmaata]

Your examples are understandable. There is a problem only to the visibility of the scripts because the board is white. The written informations cannot be read clearly.
Kindly make the visual presentation clear enough next time. Thank you.

[mouncefelmarghichi]

can you make videos about expected value for two random variables

[fatriantobong]

wait...but why you multiply categorical with probability on the dice??

[krupakhandor]

You perfectly sounds like Sheldon Cooper

[vishy]

This is totally incorrect. He has calculated the average of the sample-space (i.e., set of unique observations) instead of the population. To calculate arithmetic average of the population, he would need counts of the observations. Other way of achieving this is by using probabilities (which are nothing but relative frequencies).

For a population, population average always equals the population expected value.
µ = 1/N ∑ nx = ∑ (n/N)x = ∑ px = E(x)

However, a sample average (which is not average of a sample space but the sample itself) can differ from the population expected value. There is no such thing as expected value of a sample.

For example - if I use this guy's second case, we can clearly see the expected value of the population (which the second table summarizes) is 3.7. However, if I extracted a 12 observation sample from the population, it can turn out to be something like: 3, 2, 1, 1, 2, 2, 5, 4, 4, 1, 3, 6. The average of this sample is: 2.8. Because, in this case, there is a big difference between the sample mean (2.8) and the value we expected to get (3.7), we can conclude this sample is not representative (that is, not a good mimic) of the population.

[Jess-rubd]

Such a BIG board. Such tiny writing....

[axethroughaxe]

I didnt like this. Too long, to messy and you are skipping the important stuff!