Changing hit weights moves the centroid toward the heavier cell. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Moving weight shifts the centroid

Now the left weight is 1 and the right weight is 3.

1×1+3×2=71\times1+3\times2=7
Cluster centroidWeighted hits place a centroid inside the span.w=1w=3centroidspan=1..2 mnumerator=7 mtotalWeight=4 countcentroid=7/4 mspan=1..2 m

The new centroid is seven over four meters

The same total weight 4 gives a centroid of 7 over 4 meters.

xc=74 mx_c=\frac{7}{4}\ \text{m}
Cluster centroidWeighted hits place a centroid inside the span.w=1w=3centroidspan=1..2 mnumerator=7 mtotalWeight=4 countcentroid=7/4 mspan=1..2 m