Difference between percentile and standard normal score:
The percentiles divide the given distribution into 100 equal parts. Hence, there are 99 cut points. Thus, the percentiles is known as 100-quantile.
Standard normal score:
A Standard normal score represents the number of standard deviations from the mean. It is also called standardized score.
-If the z-score takes positive value when it is above the mean.
-If the z-score takes negative value when it is below the mean.
Formula for z score for raw data is,
Here, z is a standard normal variable, X is a normal random variable with mean .
Standard normal score measures how an observation is relative to the population mean using the population standard deviation in order to define a scale. In similar way, percentile uses median as the average.