Z-Scores and Z-Score Table Flashcard

Front

What is a Z-Score?

Back

A Z-Score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation.

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How do you calculate a Z-Score?

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Z-Score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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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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What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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CCSS.HSS.ID.A.4

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What percentage of data falls below a Z-Score of 1.96 in a normal distribution?

Back

Approximately 97.5% of the data falls below a Z-Score of 1.96.

Tags

CCSS.HSS.ID.A.4

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How do you interpret a Z-Score of 0?

Back

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

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What is the purpose of a Z-Score table?

Back

A Z-Score table provides the area (probability) to the left of a given Z-Score in a standard normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

If the mean is 50 and the standard deviation is 5, what is the Z-Score for 55?

Back

Z-Score = (55 - 50) / 5 = 1.

Front

What is the Z-Score for a value that is one standard deviation below the mean?

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The Z-Score would be -1.