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

Back

-1.4

Front

Given the data set {23, 15, 4, 11, 1, 29, 3, 17}, what is the z-score for x = 30?

Back

1.82

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 40 and the standard deviation is 1.4, what is the z-score for x = 42?

Back

1.43

Front

If the mean is 45 and the standard deviation is 2.1, what is the z-score for x = 50?

Back

2.38

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 does the standard deviation affect the z-score?

Back

A larger standard deviation results in a smaller z-score for the same value of x.