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

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 the mean is 30 and the standard deviation is 5, what is the z-score for x = 35?

Back

Z-score = (35 - 30) / 5 = 1.0

Front

If the mean is 50 and the standard deviation is 10, what is the z-score for x = 40?

Back

Z-score = (40 - 50) / 10 = -1.0

Front

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

Back

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

Front

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Back

Approximately 68% of the data falls within one standard deviation of the mean.

Front

In a normal distribution, what percentage of data falls within two standard deviations of the mean?

Back

Approximately 95% of the data falls within two standard deviations of the mean.

Front

What is the z-score for x = 22 if the mean is 21 and the standard deviation is 1.3?

Back

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