Statistics How To

Z score to Percentile Calculator and Manual Methods

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Probability and Statistics Index > Critical Values > Z Score to Percentile

How do I Convert a Z Score to Percentile?

Use a calculator, like the one below, or use a table (see instructions further down) and calculate the percentile by hand. In either case, you will be more easily able to convert a z score to a percentile if you know some basics about normal distributions, like the 68 95 99.7 rule. This rule states that 68 percent of the area under a bell curve lies between -1 and 1 standard deviations either side of the mean, 94 percent lies within -2 and 2 standard deviations and 99.7 percent lies within -3 and 3 standard deviations; these standard deviations are the “z scores.”

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Basic Z Table

A Z Table has z scores and their associated areas. Once you have found the area, convert that to a percentile. This mini table shows the area for z scores in .5 increments:
z score to percentile
For example, let’s say you wanted to convert a z score of -2 to a percentile. The area listed in the table is .0227. To convert this decimal to a percentile, move the decimal point two places to the right and then add a percentage sign:
.0227 becomes 2.27%

Things become a little more tricky when you want a z score that’s not listed in the table above. In that case, you should use a more comprehensive z-table.

Z Score to Percentile Example

Z Score of 0.33
z score to percentile 3

  1. Look up the value in the left hand z-table (see image above). The area is .6293.
  2. Move the decimal point two places to the right, then add a percentage sign: 62.93%.

You may find this video useful; it explains how to find a z-score in the z-table:

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References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.


CITE THIS AS:
Stephanie Glen. "Z score to Percentile Calculator and Manual Methods" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/percentile-z-score/
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