Calculating Z-Scores

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What is a Z-score?

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A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It indicates how many standard deviations an element is from the mean.

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How do you calculate the Z-score for a population?

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The formula for calculating the Z-score for a population is: @@z = rac{x - u}{ heta}@@ where x is the value, ν is the mean, and θ is the standard deviation.

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What does a Z-score of -2.00 indicate?

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A Z-score of -2.00 indicates that the value is 2 standard deviations below the mean.

Front

If the mean is 21 and the standard deviation is 1.3, what is the Z-score for x = 22?

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What is the significance of a Z-score of 0?

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A Z-score of 0 indicates that the value is exactly at the mean.

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How do you interpret a positive Z-score?

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

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How do you interpret a negative Z-score?

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

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What is the Z-score for a value that is 3 standard deviations above the mean?

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The Z-score for a value that is 3 standard deviations above the mean is +3.00.

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What is the Z-score for a value that is 1.5 standard deviations below the mean?

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The Z-score for a value that is 1.5 standard deviations below the mean is -1.50.

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If the mean is 22 and the standard deviation is 3.1, what is the Z-score for x = 29?

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