Mark Dickinson <dicki...@gmail.com> added the comment:
> what it's correcting for is an inaccurate value of "c" [...] In more detail: Suppose "m" is the true mean of the x in data, but all we have is an approximate mean "c" to work with. Write "e" for the error in that approximation, so that c = m + e. Then (using Python notation, but treating the expressions as exact mathematical expressions computed in the reals): sum((x-c)**2 for x in data) == sum((x-m-e)**2 for x in data) == sum((x - m)**2 for x in data) - 2 * sum((x - m)*e for x in data) + sum(e**2 for x in data) == sum((x - m)**2 for x in data) - 2 * e * sum((x - m) for x in data) + sum(e**2 for x in data) == sum((x - m)**2 for x in data) + sum(e**2 for x in data) (because sum((x - m) for x in data) is 0) == sum((x - m)**2 for x in data) + n*e**2 So the error in our result arising from the error in computing m is that n*e**2 term. And that's the term that's being subtracted here, because sum(x - c for x in data) ** 2 / n == sum(x - m - e for x in data) ** 2 / n == (sum(x - m for x in data) - sum(e for x in data))**2 / n == (0 - n * e)**2 / n == n * e**2 ---------- _______________________________________ Python tracker <rep...@bugs.python.org> <https://bugs.python.org/issue39218> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com