Calculating Z-Scores

Front

What is a z-score?

Back

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

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 positive z-score indicate?

Back

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

Front

What does a negative z-score indicate?

Back

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

Front

If the mean is 50 and the standard deviation is 10, what is the z-score for X = 60?

Back

Z-score = (60 - 50) / 10 = 1.

Front

If the mean is 100 and the standard deviation is 15, what is the z-score for X = 85?

Back

Z-score = (85 - 100) / 15 = -1.

Front

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

Back

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

Front

How can z-scores be used to compare different datasets?

Back

Z-scores standardize different datasets, allowing for comparison of values from different distributions.

Front

What is the z-score for a value that is 2 standard deviations above the mean?

Back

The z-score is +2.

Front

What is the z-score for a value that is 3 standard deviations below the mean?

Back

The z-score is -3.