# Discuss the difference and similarity between percentile and standard score norms.

Discuss the difference and similarity between percentile and standard score norms.
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Step 1
Difference between percentile and standard normal score:
Percentile:
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,
$z=\frac{X-\mu }{\sigma }$
Here, z is a standard normal variable, X is a normal random variable with mean $\mu \phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}s\mathrm{tan}darddeviation\sigma$.
Step 2 Similarities:
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.