Three centroid rows keep the same two positions and move the checked centroid marker by changing only the hit weights.
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=3
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=5
Equal weights center the marker
Weights 2 and 2 on positions 2 m and 6 m give numerator 16 and total weight 4.