Standard Deviation & Variance

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

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What is Variance?

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Variance is the average of the squared differences from the mean. It quantifies how much the numbers in a data set differ from the mean of the data set.

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How do you calculate the variance of a data set?

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

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What is the relationship between standard deviation and variance?

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The standard deviation is the square root of the variance. This means that if you know the variance, you can find the standard deviation by taking the square root.

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What is the formula for calculating standard deviation for a population?

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The formula for population standard deviation is: σ = √(Σ(xi - μ)² / N), where μ is the mean, N is the number of data points, and xi represents each data point.

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What is the formula for calculating standard deviation for a sample?

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The formula for sample standard deviation is: s = √(Σ(xi - x̄)² / (n - 1)), where x̄ is the sample mean, n is the number of data points in the sample, and xi represents each data point.

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What does a standard deviation of 0 indicate?

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A standard deviation of 0 indicates that all the values in the data set are identical and there is no variation.

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Calculate the standard deviation of the following data: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.

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0

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Calculate the standard deviation of the following data: 7, 8, 10, 10, 11, 12, 13, 14, 14, 14. Round to the nearest hundredth.

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2.41

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If the standard deviation of a data set is 4, what is the variance?

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16