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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 ”

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variance and standard deviation
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
variance dispersion
Variance, Dispersion

Variance. Dispersion

Text Example1. 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