Z-score Practice

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.

Front

How do you calculate a Z-score?

Back

Z-score = (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 indicate?

Back

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

Front

What does a positive Z-score indicate?

Back

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

Front

What does a negative Z-score indicate?

Back

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

Front

If a woman's height has a mean of 63.6 inches and a standard deviation of 2.5 inches, what is her height if her Z-score is 2.56?

Back

Height = μ + (Z * σ) = 63.6 + (2.56 * 2.5) = 70 inches.

Front

What is the Z-score for a teenage male with a waist size of 33 inches, given the mean is 29 inches and the standard deviation is 2 inches?

Back

Z-score = (33 - 29) / 2 = 2.

Front

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

Back

The Z-score is -2.00.

Front

If a national achievement test has a mean score of 100 and a standard deviation of 15, what score corresponds to a Z-score of 1.20?

Back

Score = μ + (Z * σ) = 100 + (1.20 * 15) = 118.

Front

How do you compare scores from different tests using Z-scores?

Back

You can compare scores by calculating the Z-scores for each score, which standardizes them based on their respective means and standard deviations.