How to represent data using a Q-Q plot?

A Q-Q plot is a graphical tool used to represent data and compare it to a theoretical distribution.

To create a Q-Q plot, first, the data must be sorted in ascending order. Then, the corresponding quantiles of the theoretical distribution are calculated and plotted against the sorted data. If the data follows the theoretical distribution, the points on the plot will fall along a straight line. If the data deviates from the theoretical distribution, the points will fall away from the line.

For example, suppose we have a set of data that we suspect follows a normal distribution. We can create a Q-Q plot to compare the data to the normal distribution. First, we sort the data in ascending order. Then, we calculate the corresponding quantiles of the normal distribution using a standard normal table or a calculator. We plot the sorted data against the calculated quantiles on a graph.

If the data follows a normal distribution, the points on the Q-Q plot will fall along a straight line. If the data deviates from the normal distribution, the points will fall away from the line. We can use the Q-Q plot to identify any outliers or skewness in the data.

Overall, a Q-Q plot is a useful tool for visualising and comparing data to a theoretical distribution. It can help us to identify any deviations from the expected distribution and make informed decisions about the data.