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, expressed in terms of standard deviations from the mean.

Front

How do you calculate a z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a negative z-score indicate?

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A negative z-score indicates that the value is below the mean of the data set.

Front

What does a positive z-score indicate?

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A positive z-score indicates that the value is above the mean of the data set.

Front

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

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Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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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 in a normal distribution.

Front

What is the empirical rule in statistics?

Back

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

Front

How do you interpret a z-score of 2.56?

Back

A z-score of 2.56 indicates that the value is 2.56 standard deviations above the mean.

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean; a smaller standard deviation indicates that the data points are closer to the mean.

Front

How can you use z-scores to compare different data sets?

Back

Z-scores allow for comparison of values from different data sets by standardizing them, making it possible to see how far a value is from its own mean in terms of standard deviations.