Z-score, percentile, and empirical rules

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean of a distribution.

Front

How do you calculate a Z-score?

Back

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

Front

What does a Z-score of 0 mean?

Back

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

Front

What is a percentile?

Back

A percentile is a measure used to indicate the value below which a given percentage of observations fall.

Front

What is the 33rd percentile?

Back

The 33rd percentile is the value below which 33% of the data falls.

Front

What is the empirical rule?

Back

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

Front

What percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34% of the data falls between the mean and one standard deviation above the mean.

Front

If a Z-score is -0.44, what percentile does it correspond to?

Back

A Z-score of -0.44 corresponds to approximately the 33rd percentile.

Front

What is the mean and standard deviation of a normal distribution?

Back

The mean is the average of the data, and the standard deviation measures the dispersion of the data around the mean.

Front

In a normal distribution, what is the range that contains approximately 95% of the data?

Back

The range is within two standard deviations from the mean.