Expected Value and Standard Deviation

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What is Expected Value?

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The Expected Value (EV) is the average outcome of a random variable, calculated by multiplying each possible outcome by its probability and summing the results.

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CCSS.HSS.MD.A.2

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How do you calculate Expected Value?

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EV = (Outcome1 * Probability1) + (Outcome2 * Probability2) + ... + (OutcomeN * ProbabilityN)

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CCSS.HSS.MD.A.2

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What is Standard Deviation?

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Standard Deviation is a measure of the amount of variation or dispersion in a set of values. It indicates how much individual data points differ from the mean.

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How do you calculate Standard Deviation?

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1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Find the average of these squared differences. 4. Take the square root of that average.

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What is the formula for variance?

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Variance = (Sum of (each value - mean)²) / (number of values)

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What does a higher Standard Deviation indicate?

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A higher Standard Deviation indicates that the data points are spread out over a wider range of values.

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What does a lower Standard Deviation indicate?

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A lower Standard Deviation indicates that the data points tend to be closer to the mean.

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What is the relationship between Expected Value and risk?

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The Expected Value helps assess the potential risk and reward of an investment or decision by providing a weighted average of possible outcomes.

Tags

CCSS.HSS.MD.B.5B

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How can Expected Value be used in decision making?

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Expected Value can guide decisions by comparing the EV of different options, helping to choose the one with the highest potential return.

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CCSS.HSS.MD.B.5B

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What is a probability distribution?

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A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4