Question

What is the unit of a z-score?

Answer 1

Hint: The formula of calculating the z-score is \[z=\dfrac{\left( x-\mu \right)}{\sigma }\] in which \[x\] is raw mean, \[\mu \] is the population mean and \[\sigma \] is the population standard deviation. We can understand from the formula that z is simply the difference between the raw score and the population mean.

Complete step-by-step answer:
Now let us learn about the z score. The z-score describes the position of the raw score which is deviated from the mean. The z-score is positive for those if the value is above the mean and negative if the value is less than the mean. The z-score is used to standardize the normal distribution as it helps in comparison.
The z-score is unit less which means it does not have units. They are unit less because the standard deviation is divided into the difference between mean and observation.
Let us consider the z-score \[z=\pm 1\], this represents the region under the probability curve. If the z-score is equal to zero, it means that the data point is close to the average. If the data point is equal to \[3\] or \[-3\], then it is considered as unusual. A high z-score indicates that low probability of data above z-score.

Note: If the z-score is equal to zero, it means that it is on the mean. If the z-score is equal to one, it means that it is one standard above the mean level. In the same way, If the z-score is equal to two, then it means that it is 2 standards above the mean level.