Population Variance V(X) and Standard Deviation (Q1c-d)
Variance for a probability distribution differs (in its calculation) from the variance you learned in Chapter 4. In this video, I extend the tabular approach that I used in the previous video (to find the expected value) in order to find the variance of x.
Variance formula for DISCRETE random variables is:
Variance of X:
Order of operations is very important here:
1st » Brackets: (x – μ)
2nd » Exponents: (x – μ)²
3rd » Division: … no division in this formula…
4th » Multiplication: (x – μ)² x P(x) « multiplication symbol normally hidden
5th » Addition: Σ(x – μ)²P(x)
6th » Subtraction: … completed within brackets
The standard deviation is the same here as in every other chapter. It is simply the square-root of the variance:
Standard Deviation of X:
Test your understanding:
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