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What is the Empirical Rule?

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The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 1 standard deviation of the mean according to the Empirical Rule?

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68%.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 2 standard deviations of the mean according to the Empirical Rule?

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95%.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 3 standard deviations of the mean according to the Empirical Rule?

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99.7%.

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CCSS.HSS.ID.A.4

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What percentage of people are more than 2 standard deviations above the mean?

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2.5%.

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CCSS.HSS.ID.A.4

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What percentage of people are more than 3 standard deviations above the mean?

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.15%.

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CCSS.HSS.ID.A.4

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What does it mean for data to be 'one standard deviation above the mean'?

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It means the data point is greater than the mean by an amount equal to one standard deviation.

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In a normal distribution, what does the area under the curve represent?

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The area under the curve represents the total probability of all outcomes, which equals 1 (or 100%).

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CCSS.7.SP.C.7A

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What is a standard deviation?

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A standard deviation is a measure of the amount of variation or dispersion in a set of values.

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How do you calculate the standard deviation?

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To calculate the standard deviation, find the mean of the data set, subtract the mean from each data point, square the result, find the average of those squared differences, and then take the square root.