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?

Back

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?

Back

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

Front

What is Variance?

Back

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?

Back

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

Tags

CCSS.6.SP.B.5C

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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.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

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

Back

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

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CCSS.HSS.ID.A.4

Front

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.

Tags

CCSS.HSS.ID.A.4