Instead, we refer to probability densities and distribution functions . When the area of a histogram is standardized to 1, the histogram becomes a probability density function. It is also the probability that an individual selected at random will have a value in the designated region. Strictly speaking, the histogram is properly a density , which tells you the proportion that lies between specificed values. It is a curve whose value is the proportion with values less than or equal to the value on the horizonal axis, as the example to the left illustrates.
Densities have the same name as their distribution functions.
For example, a bell-shaped curve is a normal density. Observations that can be described by a normal density are said to follow a normal distribution. If you understand that population histograms describe the way individual observations behave, you're well on your way to understanding what statistical methods are all about. One of the jobs of the mathematical statistician is to describe the behavior of things other than individual observations. If we can describe the behavior of an individual observation, then perhaps we can describe the behavior of a sample mean or a sample proportion or, even, the difference between two sample means.