Standard Deviation & Z-Scores

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

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What is a Z-Score?

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A Z-Score indicates how many standard deviations an element is from the mean. It is calculated by subtracting the mean from the value and then dividing by the standard deviation.

Tags

CCSS.6.SP.A.2

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How do you calculate a Z-Score?

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Z-Score = (Value - Mean) / Standard Deviation.

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What does a Z-Score of 0 indicate?

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A Z-Score of 0 indicates that the value is exactly equal to the mean.

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What does a positive Z-Score indicate?

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A positive Z-Score indicates that the value is above the mean.

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What does a negative Z-Score indicate?

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A negative Z-Score indicates that the value is below the mean.

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If the mean is 50 and the standard deviation is 10, what is the Z-Score for a value of 65?

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Z-Score = (65 - 50) / 10 = 1.5.

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If the mean is 40 and the standard deviation is 5, what is the Z-Score for a value of 45?

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Z-Score = (45 - 40) / 5 = 1.

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What does a standard deviation of 0 mean?

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A standard deviation of 0 means there is no spread of data; all values are identical.

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What is the Z-Score for a value that is 2 standard deviations below the mean?

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The Z-Score would be -2.00.