Final answer:
The most common numerical description of a distribution is the normal distribution, characterized by a bell-shaped curve and defined by its mean (μ) and standard deviation (σ). The uniform distribution and various discrete probability distributions like binomial and Poisson are also important but serve different purposes.
Step-by-step explanation:
The most common numerical description of a distribution in statistics is the normal distribution, which is also known as the Gaussian distribution.
This continuous probability distribution is characterized by its bell-shaped curve, which indicates that data tends to cluster around a central mean value, with a decrease in occurrence as one moves away from the mean in either direction.
The mean (μ) and the standard deviation (σ) are two key parameters that define the shape of the normal distribution. The normal distribution is significant in numerous fields, including psychology, business, economics, sciences, and many more.
It is so ubiquitous that it's also known as the "bell curve" in common parlance. In a perfectly normal distribution, approximately 68 percent of the data falls within one standard deviation of the mean, 95 percent within two standard deviations, and over 99 percent within three standard deviations.
This is referred to as the Empirical Rule. However, it's important to note that the empirical rule applies strictly to distributions that are perfectly bell-shaped and symmetric.
Another key distribution in statistics is the uniform distribution, which differs from the normal distribution in that it is concerned with events that are equally likely to occur, and its graph is a flat, horizontal line indicating a constant probability. There are also a number of discrete probability distributions, including binomial, geometric, hypergeometric, and Poisson, though not all of these are covered in elementary statistics courses.