A mean of 0 indicates that the average value of a dataset is zero. This can happen in a couple of scenarios: either the positive and negative values in the dataset perfectly balance each other out, or all values in the dataset are zero.
For example, consider a simple dataset consisting of the numbers -1, 0, and 1. If you add these numbers together, you get -1 + 0 + 1 = 0. When you divide this sum by the number of values (which is 3), you arrive at a mean of 0. This illustrates how the contributions of positive and negative values can cancel each other out.
In another scenario, if you have a dataset where all the values are zero—such as 0, 0, 0—then the mean is also 0 because the sum is 0 and the number of entries is not zero.
Understanding the context in which a mean of 0 appears is crucial, as it can signify balance or simply indicate that there is no variation when all values are the same.