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 calculating 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 is the relationship between Standard Deviation and Variance?

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Standard Deviation is the square root of Variance. If the variance is known, the standard deviation can be easily calculated.

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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 the Standard Deviation affect the shape of a distribution?

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A smaller standard deviation results in a steeper peak in the distribution curve, while a larger standard deviation results in a flatter curve.

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What is the mean of the data set: 8, 7, 5, 9, 6, 13?

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The mean is 8.

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What is the median of the data set: 4, 2, 7, 4, 3?

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The median is 4.

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If the Standard Deviation of a data set is 4, what is the Variance?

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The Variance is 16.