# Z Statistic 1 definitions

### Z Statistic

"Z statistic": A commonly used transformation of a standard normal distribution. The resulting distribution has a mean of 0 and a standard deviation of 1. Used extensively in hypothesis testing. Also known as the Z score. So for example if a data point has a Z score (or Z statistic) of -1. 64, then it lies 1. 64 standard deviations below the mean. The Z score is calculated as the difference between the data point (X) and the mean E[x], all divided by the standard deviation of the population (SD). For example if: the mean (E[x]) of a population = 100; the standard deviation (SD) = 10; and a given observation (or data point) = 83. 6; then the Z score (Z) is calculated as: Z = (X - E[x]) /SD = (83. 6 - 100 = -16. 4) /10 = - 1. 64 standard deviations. In this case the Z score is negative, indicating that the data point (83. 6) lies below the mean (of 100).