# Normal Plot (visual test for normality)

I wish to construct a Normal Plot to visually test for normality of data. My data is:

{188,199,171,200,219,172,235,194,234,206}

And needs to be plotted to look something like this:

Whereby the data points are sorted from low to high and then plotted against the mid-point of their probability bins. So, in this case there are 10 data points so 10 bins with mid points of 5%, 15%, 25% etc. For this data, you would then see the lowest value (171) plotted at (171,5%), the next value (172) plotted at (172,15%) and so on.

Any ideas where I can find the answers?

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So the values of the list (sorted) are placed on the horizontal axis. Can you give us the formula for calculating the y-axis values? Once this is specified, the plot is straightforward. – bill s Mar 28 '13 at 7:35
You might be looking for ProbabilityScalePlot. – Andy Ross Mar 28 '13 at 14:11
@bill s There are many formulas possible; a common one is InverseCDF[NormalDistribution[0, 1], y = Range[1/2, n + 1/2]/(n + 1)]] / where n is the length of the sorted data list. The y-axis ticks are labeled with 100 y. – whuber Mar 28 '13 at 16:19

I believe this ProbabilityScalePlot does what you are looking for.

data = {188, 199, 171, 200, 219, 172, 235, 194, 234, 206};

ProbabilityScalePlot[data, GridLines -> Automatic, GridLinesStyle -> "Classic"]


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This is available beginning in Version 9. – whuber Mar 28 '13 at 16:16
@whuber Actually, it was version 8. But worth pointing out nonetheless. – Andy Ross Mar 28 '13 at 16:18
Not quite /// the vertical axis scaling is very different to what the OP seeks. – wolfies Mar 28 '13 at 16:43
ProbabilityScalePlot[data,"Normal", GridLines-> {Range[170,230,15],Range[5,95,5]}, PlotRange-> {Automatic,{0.1,99.9}}, PlotMarkers-> Style["\[FilledSquare]",Darker[Orange]]] provides the cosmetic change needed to more closely match the original picture. – chuy Mar 28 '13 at 20:24
Excellent! Thanks team. I didn't find the ProbabilityScalePlot in my search but it is exactly what I was after. – CrustyNoodle Mar 29 '13 at 10:43