In univariate‏ ‏statistical analysis, if the class width is variable, we represent the distribution by a histogram of densities instead of frequencies, for a better visualisation of the data.

So far, so good.

What i am having a problem with is construction of the polygon of such a histogram. In the case where class width is constant, we join the points of abscissa= classmark (midpoint of class) and ordinate= class frequency. Then we join the polygon to zero.

As a result, we get (we must get) a polygon of enclosed area = area enclosed by the histogram.

However, if we follow these steps in case where class width is not constant, this doesn't happen.

Then, what should we do? It is obvious it isn't the same way to construct the polygon in those 2 cases.


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