G. Weight a Minute...

1. Everything's the Same

So far, when discussing the mean, standard deviation, and error in the mean, we've only dealt with equal quality measurements. All such examples used measurements made by the same personnel, using the same equipment, under the same conditions (the three error sources), the mean was simply the measurements sum divided by their number.

But what if the set consists of varying quality measurements? For example, a distance measured three times using a Total Station (TS) (242.15, 241.16, 242.14) and three more times using a fiberglass tape (242.05, 242.29, 242.38). It's reasonable, just on their spread alone, to assume the TS measurements are more accurate than the tape's. However, adding them and dividing by 6 treats the measurements the same:

(242.15+241.16+242.14+242.05+242.29+242.38) / 6 = 242.495