z-score

Front

What is a z-score?

Back

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It indicates how many standard deviations an element is from the mean.

Front

How is the z-score calculated?

Back

The z-score is calculated using the formula: z = (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 30 and the standard deviation is 5, what is the z-score for x = 35?

Back

z = (35 - 30) / 5 = 1.

Front

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

Back

z = (40 - 50) / 10 = -1.

Front

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

Back

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

Front

In a normal distribution, what percentage of values lie within one standard deviation of the mean?

Back

Approximately 68% of values lie within one standard deviation of the mean in a normal distribution.

Front

In a normal distribution, what percentage of values lie within two standard deviations of the mean?

Back

Approximately 95% of values lie within two standard deviations of the mean in a normal distribution.

Front

In a normal distribution, what percentage of values lie within three standard deviations of the mean?

Back

Approximately 99.7% of values lie within three standard deviations of the mean in a normal distribution.