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Expected Values US 5258 3 Credits Internal Finding the Variance

This guide explains how to calculate variance, a statistical measure of spread, using coin values as examples. You will learn to multiply values in designated columns, square these values, and sum the results to find the variance. We provide step-by-step calculations for several examples, including coins of different denominations, to illustrate how to use the formula VAR(X) = Sum(X² * p) - μ² effectively. Mastering variance calculations is crucial for understanding the distribution and spread of data.

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Expected Values US 5258 3 Credits Internal Finding the Variance

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  1. Large spread Expected Values US 5258 3 Credits Internal Finding the Variance The questions in the assessment will also ask you to find the variance, which is a measure of spread Small spread

  2. Multiply the values in the x column by the values in the p column Multiply the values in the X 2 column by the value in the p column Add this column up Finally, add this column up Square the values in the x column To find the variance, use the total of the last column, X 2 * p, and subtract the square of the total of the 3rd column, 2 The variance, VAR(X) = Sum(X 2 * p) - 2

  3. (These are the same examples from the Expected Values PowerPoint) Example 1: 10 coins are placed in a bag, three 10 cents, 5 20 cents and two 50 cents. What is the variance of the coins values? The variance, VAR(X) = Sum(X 2 * p) - 2 = 730 – 232 = 201

  4. Example 2: Find the variance from the following table VAR(X) = Sum(X 2 * p) - 2 = 290 – 162 = 34

  5. Example 3: Find the variance from the following table Var(X) = Sum(X 2 * p) - 2 = 7.125 – 2.3752 = 1.48

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