Histograms and probability density functions
Categorical and discrete populations can be described by probabilities and bar charts in the same way as samples. However describing the distribution of values in a continuous numerical population is not quite so easy.
The Law of Large Numbers and histograms
The Law of Large Numbers states that sample proportions always approach the underlying population probabilities as the sample size increases. We now explain the idea of a probability density function by considering how histograms change with increasing sample size .
The limiting 'infinite sample' smooth histogram is the probability density function of the population.