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 - mean) / standard deviation

Front

If the mean is 22 and the standard deviation is 3.1, what is the z-score for x = 29?

Back

Z-score = (29 - 22) / 3.1 = 2.26

Front

Given the dataset {1, 9, 16, 7, 2, 23}, what is the z-score for x = 5?

Back

Z-score = (5 - mean) / standard deviation = -0.61

Front

For the dataset {15, 9, 27, 29, 37, 17, 30}, what is the z-score for x = 14?

Back

Z-score = (14 - mean) / standard deviation = -1.02

Front

If the mean is 29.8 and the standard deviation is 7, what is the z-score for x = 20?

Back

Z-score = (20 - 29.8) / 7 = -1.4

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 21 and the standard deviation is 1.3, what is the z-score for x = 22?

Back

Z-score = (22 - 21) / 1.3 = 0.77

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.