Is a probability density funcion a function that represents a density histogram?

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Where " density " , plotted on the y-axis is defined as the value derived by deviding the frequency of a class by the total number of data by the class interval?

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A probability density function $f_X$ is not a histogram. What it says is $P(X \in [a,b])=\int_a^b f_X(x) dx$. Nothing more, nothing less.

However, one can convert a histogram into a probability density function, by choosing your units so that the total area under the histogram is $1$ and the area under each bar of the histogram is proportional to the number of samples appearing in the corresponding range. Then you can have a piecewise constant function (given by the height along the histogram) which will now be a probability density function. This can be useful for things like approximating a distribution from a sample, especially if you know the true distribution should be continuous.

But most probability density functions that we see in practice do not arise in this way, at least not directly.