Normality is a statistical concept that refers to the degree to which a set of data conforms to a normal distribution, which is a symmetrical, bell-shaped curve. A normal distribution is characterized by the fact that the majority of the data points are concentrated around the mean, with fewer and fewer data points as you move further away from the mean in either direction.

There are several reasons why normality is an important concept in statistics. First, many statistical tests and procedures assume that the data are normally distributed, so it is important to ensure that this assumption is met in order to get valid results. Second, normality can be used as a benchmark for comparing the distribution of a set of data to other distributions, which can be helpful in understanding the characteristics of the data and how it might behave in different situations.

Here are two examples of normality:

Example 1: Heights of adult men

Imagine that you are studying the heights of adult men in a certain population. You collect data from a random sample of 1000 men and plot the results on a histogram. The resulting distribution looks like a bell-shaped curve, with the majority of the heights concentrated around the mean and fewer and fewer heights as you move further away from the mean in either direction. This distribution would be considered normal because it conforms to the symmetrical, bell-shaped curve characteristic of a normal distribution.

Example 2: Test scores

Imagine that you are a teacher and you give a test to your students. You collect the scores and plot them on a histogram. The resulting distribution looks like a bell-shaped curve, with the majority of the scores concentrated around the mean and fewer and fewer scores as you move further away from the mean in either direction. This distribution would be considered normal because it conforms to the symmetrical, bell-shaped curve characteristic of a normal distribution.

In both of these examples, the data conform to a normal distribution, which means that they are considered to be normal. This is important because it allows us to use statistical tests and procedures that assume normality, such as the t-test and ANOVA, in order to make inferences about the data.

It is worth noting that not all data will conform to a normal distribution, and it is important to be aware of this when choosing statistical tests and procedures. For example, if you were studying the income of a group of people and the distribution of the data was skewed to the right (with a long tail on the high end), this would not be considered a normal distribution and you would need to use statistical tests and procedures that are appropriate for non-normal data.