Kevin E. answered • 10/02/19
A chemist going back to school for cyber security.
This stems from the fact that the higher the mean, the higher the probability of a single data point which is smaller than the mean being further from the mean.
For example, if the average heart rate is on the low end of the normal spectrum (62 bpm for example), a difference of -20 bpm or more negative (heart rate of 42 bpm or less) is exceedingly unlikely, biologically speaking. If we went to the higher end of the normal range (98 bpm for example), having a difference of -20 bpm or more negative (making it 78 bpm or less) is far more likely now, biologically speaking.
This difference is the (xi-µ)2 calculation in the numerator that is part of adding everything together. And since the -20 or more negative is more likely with the higher heart rate, that data points corresponding to 78 bpm or less with the 98 bpm average will happen more frequently than then the 42 bpm or less with the 62 bpm mean. This means more entries of adding (-20)2 and more negative numbers squared to the total before dividing by the degrees of freedom.
This is what increases the variability.
