Finding Z - Score

A z-score indicates how many standard deviations an element is from the mean of a distribution.

The formula is $$z = \frac{x - \mu}{\sigma}$$ where x is the value, \mu is the mean, and \sigma is the standard deviation.

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

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

Using the formula: $$z = \frac{50 - 45}{2.1} = 2.38$$ .

Using the formula: $$z = \frac{29 - 22}{3.1} = 2.26$$ .

Z-scores describe the exact location of a score within a distribution.

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

A z-score of 1.5 means the value is 1.5 standard deviations above the mean.

A z-score of -1.25 means the value is 1.25 standard deviations below the mean.