Quantitative Usability, Statistics & Six Sigma by Jeff Sauro
Interactive Graph of the Standard Normal Curve
by Jeff Sauro | December 14, 2007 ::
RSS
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
View All Articles |
Subscribe to RSS
|
Follow on Twitter |
Get Email Updates
| December 7, 2009 | srinivasan wrote: |
| Is 3.4 ppm in 6sigma is applicable to unilateral tolerance , how |
| December 7, 2009 | srinivasan wrote: |
| Is z score and std deviation are same are different |
| December 7, 2009 | srinivasan wrote: |
| I would like to know the z score and ppm calculation for unilateral & bilateral toleraqnce |
| November 24, 2009 | ROLY B. BAYO-ANG wrote: |
| VERY INTERACTIVE SITE |
| November 13, 2009 | Christy Muth wrote: |
| What percentage of architects have Z scores (a) above .10, (b) below .10, (c) above .20, (d) below .20, (e) above 1.10, (f) below 1.10, (g) above -.10, (h) below -.10? Suppose that the scores of architects on a particular creativity test are normally distributed. What percentage of architects have Z scores (a) above .10, (b) below .10, (c) above .20, (d) below .20, (e) above 1.10, (f) below 1.10, (g) above -.10, (h) below -.10? |
| July 20, 2009 | Adell wrote: |
| I have the results of a final exam for 2 classes. I have the number of students that scored correctly on each question and the percentage. I would like to determine if the students did better on the questions that were "taught" 4th quarter compared to what they had been taught the other 3 quarters. Is a z test appropriate? |
| February 16, 2009 | anonomous wrote: |
| would be much more useful if you also include much larger z-scores |
| October 2, 2008 | Jeseme wrote: |
| How do i compute for the standard score (z-score)of the following data? How will the graph look like? 53 53 50 45 45 43 42 42 41 40 39 39 39 38 37 36 36 36 36 34 34 32 32 32 32 31 31 30 30 29 28 27 27 26 18 |
| 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! |