Measuring Usability: Interactive Graph of the Standard Normal Curve

Interactive Graph of the Standard Normal Curve
by Jeff Sauro | December 14, 2007 :: 60 Related Questions How useful was this calculator?
Avg. Rating: 84 ( 27 ) | 4 Comments

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Tag Name	#	Vote
Normal Curve	13
Z-Score	11
Two-Tailed Area	9
Bell Curve	8
bimodal	7
Graph	7
One-Tailed Area	7
Standard Normal Curve	7
Statistics	3

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Hover over the normal curve to display the area and z-score.To enter specific values use the Z-Score to Percentile Calculator or the Percentile to Z-Score Calculator.

Two-Tailed Area Under the Normal Curve

The values presented above are computed by adding up all the area under the curve(the shaded area) from the point where the mouse is hovering to its opposite-signed point. For example, by hovering over 1σ the area between -1σ and 1σ is shaded and represents about 68% of the area of the curve. This corresponds to a Z-Score of 1. The area above 1σ and below -1σ is 1 minus the proportion of area covered or about 32%. Contrast the area generated from these Z-score with the area generated below. Add any mean and standard-deviation in the boxes. As an example, a mean of 100 and SD of 16 (similiar to the distribution of IQ scores) has been added to the input boxes. We can then see that 95% of the IQ tests scores should fall between 68 and 132. To enter specific values use the Z-Score to Percentile Calculator.

One-Tailed Area Under the Normal Curve

The values presented are computed by adding up all the area under the curve(the shaded area) from negative infinity to the point where the mouse is hovering. For example, by hovering over 1σ about 84% of the area is shaded. This corresponds to a Z-Score of 1. The area above 1σ is 1 minus the proportion of area covered or about 16%. As an example, a mean of 100 and Standard Deviation of 16 (similiar to the distribution of IQ scores) has been added to the input boxes. So for example, if you scored a 132 on an IQ test, you would have an IQ higher than over 97% of the popultation (a z-score of 2). To enter specific values use the Percentile to Z-Score Calculator.

A Note about the Calculations & Decimal Precision

The values presented in the graphs above are approximations derived from the work of Abramowitz & Stegun. If you need precision to more that 3 decimals you are encouraged to consult multiple published tables of Z-Values.If you need to look up specific values then you will most likely find it easier to use the Z-Score to Percentile Calculator and the Percentile to Z-Score Calculator

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Related Questions

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	Jeff: Can you possibly share the actual formula you are using in this application to produce the Adjusted Wald calculations? Thanks
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March 19, 2008 | Kevin Horton wrote:

Jeff, great website. Do you happen to have a page that calculates 95% CIs for percentiles (i.e. 95th percentile)? Thanks.

February 22, 2008 | Robert wrote:

What is the difference between z-score and standard deviation?

January 11, 2008 | Sugato Banerjee wrote:

Beautiful but i wish the graph would cover 6 sigma level too

January 10, 2008 | Sterling Gardiner wrote:

This is just awsome. . .make stats much easier! Thanks!

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