How do I create/calculate the probability density curve in a histogram which is scaled to the frequency axis with ABSOLUTE values (example)? The curve should be based on the calculated average and the deviation.
Thanks!
1 Answer
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I found it myself finally:
As known the relative frequency $H$ at a certain value $x$ is calculated by the probability density function:
$$ H = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$
- with $\mu$ as the average value
- $\sigma$ as the standard deviation
in order to create a density curve which is scaled to a histogram the class width $K$ used in the histogram is needed. Now the absolute frequency for a class width $K$ at a certain value $x$ is now simply calculated by:
$$ H = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}Kn $$
- with $K$ as the used class width in the histogram
- $n$ as the total number of values
So, in order to fit the ideal Gaussian curve for normal distributed values in the histogram with absolute frequencies the class width $K$ is needed.