Variance and Standard Deviation of Discrete Random Variables (Jump to: Lecture | Video )

To calculate the variance of a discrete random variable, we must first calculate the mean. Here is the mean we calculated from the example in the previous lecture:

Figure 1.

Now, we can move on to the variance formula:

Figure 2.

To find the first part of the equation, we first square every "x". Then, we multiply each squared "x" by "P(x)". Last, we add together all resulting values.

Figure 3.

We find the first part of the equation to be 7.75. Now, we can plug in the rest of the values to get our answers:

Figure 4.

The variance is 0.73, while the standard deviation is 0.85.