1. Variance and Standard Deviation The Expected Value of a random variable gives the average value of the distribution The Standard Deviation shows how spread out the data is You can think of the standard deviation as “the average distance of the data from the average” The Variance is the square of the standard deviation Variance of discrete random variable Variance of continuous random variable

2. Variance, Dispersion Text Example 1. Suppose that we put 20 slips of paper, bearing the following numbers, into a box. 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6 Let X be number on a slip that is drawn, at random, from the box. We put 20 slips of paper, bearing the following numbers, into a second box and let Y be the number on a slip that is drawn, at random, from that box. 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7 Variance. Dispersion

4. For X and Y from Example 1, we have