When assessing a dataset's normality, what does a non-linear probability plot indicate?

A non-linear probability plot suggests that the data does not conform to a normal distribution. In a probability plot, if the data points align closely along a straight line, it indicates that the underlying distribution is approximately normal. However, if the plot shows a non-linear pattern, this deviation signifies that the data fails to meet the characteristics of normality.

Normal distributions are symmetric, and their bell-shaped curve leads to a linear representation on such plots. When there is curvature or a specific pattern that diverges from a straight line, it points to the presence of skewness, kurtosis, or other irregularities within the data. Thus, the conclusion that the variable is not approximately normally distributed is substantiated by the evidence from the plot showing this non-linear behavior.

In contrast, the other options imply properties of the data that don’t hold true when a non-linear trend is observed; for instance, the mean and median being equal or the absence of outliers wouldn’t inherently lead to such a finding on the plot.