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

highlighted = computed this step

Left weight pulls the centroid left

Weights 3 and 1 on positions 2 m and 6 m give numerator 12 and total weight 4.

xc=12/4=3x_c=12/4=3
Cluster centroidWider source positions show the weighted marker shift clearly.w=3w=1centroidspan=2..6 mnumerator=12 mtotalWeight=4 countcentroid=3 mspan=2..6 m

Right weight pulls the centroid right

Weights 1 and 3 on positions 2 m and 6 m give numerator 20 and total weight 4.

xc=20/4=5x_c=20/4=5
Cluster centroidWider source positions show the weighted marker shift clearly.w=1w=3centroidspan=2..6 mnumerator=20 mtotalWeight=4 countcentroid=5 mspan=2..6 m

Equal weights center the marker

Weights 2 and 2 on positions 2 m and 6 m give numerator 16 and total weight 4.

xc=16/4=4x_c=16/4=4
Cluster centroidWider source positions show the weighted marker shift clearly.w=2w=2centroidspan=2..6 mnumerator=16 mtotalWeight=4 countcentroid=4 mspan=2..6 m