Cluster Centroids

Cluster Span Bounds the Centroid

The centroid must remain inside the checked cluster span. 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 span comes from the endpoint positions

The cluster endpoints are 1 meter and 2 meters.

1 m≤x≤2 m1\ \text{m}\le x\le2\ \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

The centroid must lie inside that span

The centroid 5 over 4 meters is between the endpoints.

1≤54≤21\le\frac{5}{4}\le2
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