Standard Deviation

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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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How is Standard Deviation calculated?

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Standard Deviation is calculated by taking the square root of the variance. Variance is the average of the squared differences from the Mean.

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What is Variance?

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Variance is a statistical measurement that describes the spread of numbers in a data set. It is calculated as the average of the squared differences from the Mean.

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What is the formula for Variance?

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Variance (σ²) = Σ (xi - μ)² / N, where xi is each value, μ is the mean, and N is the number of values.

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What does a Standard Deviation of 0 indicate?

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

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How does Standard Deviation relate to the Normal Distribution?

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In a normal distribution, about 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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What is the relationship between Standard Deviation and data spread?

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A larger Standard Deviation indicates a wider spread of data points from the mean, while a smaller Standard Deviation indicates that the data points are closer to the mean.

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Calculate the Standard Deviation for the data set: {10, 19, 38, 50, 51}.

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Standard Deviation = 15.84.

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Calculate the Variance for the data set: {5, 10, 7, 12, 0, 20, 15, 22, 8, 2}.

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Variance = 52.77.

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What is the Mean of the data set: {5, 11, 2, 12, 4, 2}?

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Mean = 6.