Mean & Variance Visually Explained

Added: 2026-05-20

[00:00:00]The mean of a distribution, often denoted with a Greek letter mu, is a way of capturing the center of mass for that distribution.

[00:00:07]>> [music] >> It's calculated as the expected value of our random variable, which is a way of saying you go through all of the different possible outcomes, and you multiply the probability of that outcome times the value of the variable. If higher values are more probable, that weighted [music] sum is going to be bigger. If lower values are more probable, that weighted sum is going to be smaller.

[00:00:27]A little more interesting is if you want to measure how spread out [music] this distribution is, because there's multiple different ways you might do it.

[00:00:33]One of them is called the variance. The idea there is to look at the difference between each possible value and the mean, square that difference, and ask for its [music] expected value. The idea is that whether your value is below or above the mean, when you square that difference, you get a positive number, and the larger the difference, the bigger that number. Another way to measure spread >> [music] >> is what's called the standard deviation, which is the square root of this value.

[00:00:57]That can be interpreted much more reasonably as a distance on our diagram, and it's commonly denoted with the Greek letter sigma, though you know, M for mean, S for standard deviation, but both in [music] Greek.