Cluster Centroid Is Weighted Average - Detector Physics: Timing and Spatial Reconstruction Step by Step

Picture two neighboring detector strips at 1 meter and 2 meters with hit weights 3 and 1. The centroid ledger multiplies position by weight, divides by the total weight 4, and lands at 5/4 meters; real strip clusters also carry calibration, charge-sharing, threshold, noise, and alignment uncertainty.

A cluster centroid is a finite weighted average. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The centroid numerator is a weighted sum

Position 1 meter has weight 3, and position 2 meters has weight 1.

3\times1+1\times2=5

Divide by total weight to place the centroid

Total weight is 4, so the centroid is 5 over 4 meters.

x_c=\frac{5}{4}\ \text{m}