Wiley Horne
The way I learned it (I think )is that if you’re sampling from the same population—like ‘how many Ford 150’s were sold each day in the US’—and the Groups are months, say—and you assume normal distribution—then you could calculate a variance for each month (and its square root is the std. dev. for that month). And if you sum the variances of all the months and take that square root, you have the std. dev. for the whole year. You couldn’t just average the std. deviations across Groups (months in this case)—which I think is your point.

In the present case of the chisels, I never saw what the groups are, or how many observations are being made, so who knows what it means.

Wiley...wondering if he recalls it correctly