Geometric Mean Calculator

The geometric mean is the nth root of the product of n positive numbers, and it is the right average when the values multiply rather than add. Paste a list and you get the geometric mean together with the arithmetic mean, the harmonic mean, the product and the multiplicative spread; a second mode takes a weight for each value. Everything is worked through logarithms, so a long list does not overflow the way multiplying it out would. Values must be greater than zero, because a zero collapses the product and a negative makes the root undefined.