Six Sigma – iSixSigma Forums Old Forums General Question About Histogram

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• #37210

Ripley
Member

Perhaps this is an odd question, but here goes…
Why do some of the data bars within a histogram physically extend above the drawn distribution curve?  Why wouldn’t the drawn (red) distribution curve rest above the tops of all of the data bars?

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#109037

mpl
Participant

I think it just depends on your statistics package.  What are you using??

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#109043

aBBinMN
Participant

What you should expect is for the area under the curve to ~ equal the area of the bars.
The curve represents the ideal theoretical model of whatever distribution you’re using (normal, Weibull, etc.) closest to your data. In reality, some data points (in this case histogram groupings) fall above while others fall below. Also, histogram bars represent descrete groupings, whereas the curve represents continuous theoretical data. Even if your data were perfectly normal, this means that at least part of your bar would be above the curve.

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#109086

RubberDude
Member

aBBinMN has a very good answer, but I wish to expound a bit.
As he said, the histogram is a discrete data value representation.  But more importantly, you have to keep in mind that the distribution curve represents the “probability” of the process output.  It is NOT an “absolute” value.  Some people think the normal curve indicates that a certain percent of the population will fall within a range.  The BETTER definition is that each individual output from the process has the probability of falling within a range.
With the histogram, the actual number/percent of the group measured is indicated.
Hope this makes it a little clearer.

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