A statistical average is a weighted count ledger. 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 average uses every bucket count

The numerator multiplies each heads count by its multiplicity.

Hˉ=44\bar H=\frac{4}{4}
Average numeratorThe numerator is recomputed from bucket values.microstateCount=4bucketCounts=0:1|1:2|2:1probabilities=1:2/4=1/2comparisonBit=0 bitaverageNumerator=4average=1

The mean is exact

The checked mean heads count is one.

Hˉ=1\bar H=1
Exact meanThe mean label is not caller-supplied.microstateCount=4bucketCounts=0:1|1:2|2:1probabilities=1:2/4=1/2comparisonBit=0 bitaverageNumerator=4average=1