How many fruit do you need to measure?

A size estimate is only as good as the sample behind it. Statistics gives a clear answer, and it is more than most scouts measure.

Fruit within a block vary. The useful question is how many fruit are needed so that the block average is known within a margin you can live with.

The formula

For simple random sampling the required number is n = (σ·t / e)². A review of orchard fruit sizing works through an example: with a standard deviation of 25 g, an accepted error of ±5 g and 95 percent confidence, about 98 fruit are needed. The number depends on variability, not on the size of the orchard.¹

Random beats “representative”

Choosing fruit that look typical is not the same as sampling. In an apple study cited by the same review, 20 “representative” fruit picked around a tree gave a mean weight only within about 13 percent of the true mean from harvesting the whole tree.¹ Pest monitoring protocols make the same point by spreading samples across the block, such as 25 fruit from each corner for a total of 100.²

Spread the sample across trees

Models that estimate the share of each size grade from diameter measurements reached acceptable accuracy only when at least 10 trees were measured.³ At larger scale, the USDA found that 21 blocks with two trees each and about 15 fruit per tree gave a coefficient of variation of about 2 percent on mean fruit size for oranges, and Florida’s size survey of 1,200 sample trees achieved a maximum error of about 1.5 percent at 95 percent confidence.^4,5