What is the sum of the differences between sample observations and the sample mean is?

The sum of the differences between sample observations and the sample mean is always equal to zero. This is because the sample mean is calculated as the average of the observations, and when you subtract the mean from each observation, the positive and negative differences cancel each other out. Mathematically, this can be expressed as Σ(xi - x̄) = 0, where xi represents each individual observation and x̄ is the sample mean.