Standard Deviation

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What is Standard Deviation?

Back

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

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What is the formula for Standard Deviation?

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The formula is: \( \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \) where \( \mu \) is the mean, \( x_i \) are the data points, and \( N \) is the number of data points.

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What does a low Standard Deviation indicate?

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It indicates that the data points tend to be close to the mean of the set.

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What does a high Standard Deviation indicate?

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It indicates that the data points are spread out over a wider range of values.

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What is Variance?

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Variance is the square of the standard deviation and measures the spread of a set of data points.

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How is Standard Deviation related to Variance?

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Standard Deviation is the square root of Variance.

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What is the Median?

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The median is the middle value in a data set when the numbers are arranged in order.

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What is the relationship between Mean and Standard Deviation in a normal distribution?

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In a normal distribution, the mean, median, and mode are all equal, and the standard deviation determines the width of the distribution.

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What percentage of data falls within one standard deviation of the mean in a normal distribution?

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Approximately 68% of the data falls within one standard deviation of the mean.

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What percentage of data falls within two standard deviations of the mean in a normal distribution?

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Approximately 95% of the data falls within two standard deviations of the mean.