Shape of a probability density function

In practical applications, the available sample data rarely provide enough information to be sure about the shape of the underlying probability density function.

Normal distributions

One family of symmetric continuous probability density functions called normal distributions is particularly useful. Although normal distributions are only appropriate as population models for a small number of data sets, they are extremely important in statistics — their importance will be explained later in this chapter.

Shape of the normal family of distributions

The shape of the normal distribution depends on two numerical values, called parameters, that can be adjusted to give a range of symmetric distributional shapes. These parameters are called µ and σ and are the distribution's mean and standard deviation.

For some data sets, a normal distribution provides a reasonable model. The two parameters can be chosen to make the distribution's shape match that of a histogram of the data as closely as possible.

Reaction to stimulus

We will revisit normal distributions later in this chapter.