A half-normal plot is a graphical representation of data that is used to evaluate the symmetry and normality of a statistical distribution. It is a helpful tool for identifying potential outliers and determining the underlying distribution of a dataset.

To create a half-normal plot, the data is first sorted in ascending order. Then, a line is drawn from the minimum value on the x-axis to the maximum value on the y-axis. The plotted points are then divided into two halves, with one half being above the line and the other half being below.

For example, consider a dataset of 10 observations with the following values: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. The half-normal plot for this data would look like this:

In this plot, the points in the lower half fall below the line and the points in the upper half fall above the line. The distribution is symmetrical, with the same number of observations in each half.

Another example of a half-normal plot is for a dataset with the following values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. The half-normal plot for this data would look like this:

In this plot, the distribution is not symmetrical because there are more observations in the upper half than in the lower half. This indicates that the distribution is not normal and may have outliers.

Half-normal plots are useful for evaluating the symmetry and normality of a dataset because they provide a visual representation of the distribution. By dividing the points into two halves, it is easy to see if the distribution is symmetrical and if there are any potential outliers. This information can then be used to determine the underlying distribution of the data and make appropriate statistical inferences.