We know that PMF is for Discrete Random Variables whereas PDF is for Continuous Random Variables. But consider this thing. Say we are measuring the height of all women in India, now say their heights range between 130cm to 165cm. Now while collecting data we get the height of some women as 152.65341414cm, 152.8797194791cm , 152.8794917491cm. Now can we really plot them on the graph? We need to take the ceil or the floor value right? That is we are actually taking a discrete value. So while data collection even in case of a continuous random variable isn't it that we need discrete points to set up our PDF graph and from there we can actually do the continuous stuff like when asked what is the prob that height is between 150-156cm we can now integrate the f(x) obtained from the graph.
So my question is in PDF do we actually plot continuous data or we plot discrete data and from there we reach the calculations for continuity?
for example say when we work with the Irish Dataset (https://archive.ics.uci.edu/ml/datasets/iris) we plot the length of the petals like this in a graph
and from there we draw the Gaussian distribution curve, but the plotting is actually based on some discrete values.