Dec 4 B1 BW Stats Ch 2.4 Measures of Variation

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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. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

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How do you calculate the standard deviation of a data set?

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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 this average.

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What does a higher standard deviation indicate about a data set?

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A higher standard deviation indicates that the data points are more spread out from the mean, suggesting greater variability in the data.

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What is the empirical rule in statistics?

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The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

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CCSS.HSS.ID.A.4

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What percent of data falls within 1 standard deviation of the mean in a normal distribution?

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Approximately 68%.

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CCSS.HSS.ID.A.4

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What percent of data falls within 2 standard deviations of the mean in a normal distribution?

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Approximately 95%.

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CCSS.HSS.ID.A.4

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What percent of data falls within 3 standard deviations of the mean in a normal distribution?

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Approximately 99.7%.

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CCSS.HSS.ID.A.4

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If the mean of a data set is 50 and the standard deviation is 5, what is the range of values that fall within 1 standard deviation?

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The range is from 45 to 55.

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What is variance in statistics?

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Variance is the average of the squared differences from the mean. It measures how far a set of numbers is spread out from their average value.

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How is variance related to standard deviation?

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Standard deviation is the square root of variance. It provides a measure of spread in the same units as the data.