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Standard Deviation and Variance

# Standard Deviation and Variance - Standard Deviation and...

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Standard Deviation and Variance Standard deviation is the measure of dispersion or variability around an expected value. It is calculated by measuring deviations from the mean, multiplying them by their probabilities, summing them and then finding the square root. For example, let us suppose you have the opportunity to make an investment. You estimate that you have a 20% chance of a \$300 return, a 60% chance of a \$600 return and a 20% chance of a \$900 return. First you find the expected value. Potential Outcome X Probability = Weighted Value \$300 X .2 = \$ 60 \$600 X .6 = \$360 \$900 X .2 = \$180 Expected Value \$600 Now you are ready to calculate the standard deviation, as follows: Step 1 Step 2 Step 3 Step 4 Subtract the Expected Value from each Outcome Square each Answer Multiply by the Probabilities and Sum Find the Square Root 300 – 600 = (300)

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90,000 X .20 = 18,000 Square root of 36,000 = \$190 600 – 600 = 0 0 X .60 = 0 900 – 600 = 300 90,000 X .20 = 18,000 36,000 The number 36,000 above is called the variance. The square root of the variance is the standard deviation.
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Standard Deviation and Variance - Standard Deviation and...

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