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.

3×1+1×2=53\times1+1\times2=5
Cluster centroidWeighted hits place a centroid inside the span.w=3w=1centroidspan=1..2 mnumerator=5 mtotalWeight=4 countcentroid=5/4 mspan=1..2 m

Divide by total weight to place the centroid

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

xc=54 mx_c=\frac{5}{4}\ \text{m}
Cluster centroidWeighted hits place a centroid inside the span.w=3w=1centroidspan=1..2 mnumerator=5 mtotalWeight=4 countcentroid=5/4 mspan=1..2 m