Calculating Z-Scores

A z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: $$z = \frac{x - \mu}{\sigma}$$ where x is the value, \mu is the mean, and \sigma is the standard deviation.

The formula to find the z-score for a population is: $$z = \frac{x - \mu}{\sigma}$$ where x is the value, \mu is the population mean, and \sigma is the population standard deviation.

The mean of z-scores is always 0, regardless of the mean of the raw scores.

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

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

The z-score is $$z = \frac{60 - 50}{10} = 1$$ .

The z-score is $$z = \frac{3 - 7.6}{4.5} = -1.02$$ .

The formula for calculating the z-score of a sample is: $$z = \frac{x - \bar{x}}{s}$$ where x is the value, \bar{x} is the sample mean, and s is the sample standard deviation.

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

A z-score of +2 indicates that the value is 2 standard deviations above the mean.