Page 2 of 4

### 2. One of These Things is Not Like the Other

To combined different quality measurements, we use weights. A *weight* is a multiplier applied to an individual measurement based on its relative accuracy compared to other measurements.

Assume the TS's measurements are twice as good as the tape's - the TS's weight is 2, the tape's is 1. The effect would be adding each TS measurement twice, each tape measurement once for a total of 9 measuremetns:

(242.15+242.15+241.16+242.16+242.14+242.14+242.05+242.29+242.38) / 9 = 242.180

Or we could multiply each measurement by its weight, add them, then divide by the weight total:

[2(242.15)+2(241.16)+2(242.14)+1(242.05)+1(242.29)+1(242.38)] / [2+2+2+1+1+1] = 242.180

The general equation for a weighted mean is

Equation (G-1) |

And the weighted standard deviation:

Equation (G-2) |