Yield across four rows
Deciding which measure answers which question, when the obvious one is wrong twice.
Notes and data
An orchard recorded the mass of fruit picked from four rows in one season, in kilograms:
Row A: 120 Row B: 140 Row C: 130 Row D: 610
Rows A, B and C were planted in the same year and hold a similar number of trees. Row D was planted eight years earlier and has roughly five times as many mature trees as any of the others.
Answers in order, explanations withheld, and a report on where the chain broke.
- 2.1MeanFoundation
What is the mean yield across the four rows?
- A250 kg
- B135 kg
- C200 kg
- D130 kg
Show the answer and reasoningHide the reasoning
250 kg
The four values total 1000 kg, and 1000 / 4 = 250 kg.
- 2.2Centre and spreadStandard
Builds on: The mean of 250 kg from question 1, which is the number this question asks you to distrust.
Which measure better represents a typical row in this orchard, and why?
- AThe median, because Row D is far larger than the rest and pulls the mean upward.
- BThe mean, because it uses every value.
- CThe range, because it shows how much the rows differ.
- DThe mean, because the four rows are the whole orchard rather than a sample.
Show the answer and reasoningHide the reasoning
The median, because Row D is far larger than the rest and pulls the mean upward.
The mean of 250 kg exceeds three of the four rows, which is a sign it is not describing a typical one. The median of 135 kg sits between the values that resemble each other. Using every value is exactly the problem here, not a defence.
- 2.3RatesChallenge
Builds on: The recognition in question 2 that Row D is unlike the others, which is what makes a per-tree comparison the right move.
If Row D really has five times as many mature trees as each other row, roughly what is its yield per tree compared with Row B's?
- ASlightly lower than Row B's
- BAbout five times Row B's
- CAbout the same as Row B's
- DIt cannot be compared without the exact tree counts
Show the answer and reasoningHide the reasoning
Slightly lower than Row B's
Five times Row B's trees would give 5 x 140 = 700 kg at Row B's productivity. Row D produced 610 kg, which is less, so each of its trees is yielding slightly less. The raw total made Row D look far more productive; per tree it is not.