What is the Difference between z scores and percentile ranks?

Answer 1

First let's define both, that will help to see the difference.

1.A percentile is a measure that lets us know what percent of the total frequency scored below that measure. A percentile rank is the percentage of scores that fall below a given score. Here is how that works.

Given a score, call it S and a total of n scores we are looking at, we find the number of scores below S and divide that by n. Next multiply that by 100 and you have the percentile rank.

Now a z score is the number of standard deviations from the mean.
Say the mean is M and your score is S as above. Let sigma be the standard deviation of the distribution. Then z=(S-M)/sigma.

So let's say the mean M is 100 and sigma is 15. S is 132, you did better than average!
So z=(132-100)/15=2.13

If 60 percent of the people scored less than you, then you are in the 60th percentile.
Furthermore, lets say, there were 100 people taking test, then 60 of them scored less than you. Your percentile ranking is (60/100)x100=60

So both are measures of where your results falls in a distribution. z scores are often used for probability of a certain result. Percentile ranks are often used in looking at standardized test results or growth data. One can convert from one to the other.
I have given a conversion table link below

http://www.acposb.on.ca/conversion.htm