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

What is the formula for calculating a z-score for a population?

Back

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

Front

How do you interpret a positive z-score?

Back

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

Front

How do you interpret a negative z-score?

Back

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

Front

What does a z-score of 0 represent?

Back

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

Front

If the mean temperature is 23 degrees and the standard deviation is 4.2 degrees, what is the z-score for a temperature of 17 degrees?

Back

-1.43

Front

If the mean score of a class is 22 and the standard deviation is 3.1, what is the z-score for a score of 29?

Back

2.26

Front

What is the z-score for a test score of 50 if the class average is 70 and the standard deviation is 8?

Back

-2.5

Front

Calculate the z-score for a value of 11 if the mean is 27 and the standard deviation is 1.4.

Back

-11.43

Front

What does a z-score of 2.5 indicate about a data point?

Back

It indicates that the data point is 2.5 standard deviations above the mean.