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I am a retired philosopher, familiar with some of the philosophical problems about probability (e.g. Hume's problem of induction) but at a loss in calculating probabilities. I recently came across the following problem - problem for me, that is, not site users.

The number of pupils in a school in the years 2020, 2021 and 2023 was:

2020 - 200

2021 - 220

2023 - 250

On the basis of the data, probably how many were at the school in 2022?

Any help would be appreciated. I realise the answer may vary with the theory of probability used.

Geoffrey Thomas
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  • Since no information about probability is given, no information about probability can be inferred. However, a common procedure in statistics is to approximate the graph of partial (finite) data with the equation of the line having the least squared error from the given data. It is described in many places, like https://www.stats4stem.org/least-squares-regression-line. – Dan Asimov Feb 27 '24 at 18:49
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    Not sure what you are hoping for. This isn't really a math problem.... you need to model the situation. You could guess that it's increasing linearly, or use a different functional form if you prefer, but you only have 3 data points so that would just be a guess. – lulu Feb 27 '24 at 18:49
  • For all we know there may have been some catastrophic event... like a country invading or a widespread epidemic which caused school closures at that school... which could have made it such that there were zero pupils that year. The only thing we can say for certain is that there were a non-negative integer number of students. – JMoravitz Feb 27 '24 at 18:58
  • Granted, you might guess that the number of students will be between $220$ and $250$, and that might be a typically reasonable guess to make...but it will merely be a guess, and one that does not reflect reality when taken to the extremes. Supposing it appears we increase by an average of $20$ students per year... does that really suggest that this very same school will have an average of $2000000200$ students in the year $1000002220$? Very probably not. – JMoravitz Feb 27 '24 at 19:01
  • Thanks for the comments. I have taken the 'problem' from John Cohen's Chance, Skill, and Luck, an old text which I think is more concerned with the psychology of probability judgements than with strict statistical inference. It struck me that there just wasn't the data to make a safe inference. I much appreciate everyone's help. – Geoffrey Thomas Feb 28 '24 at 12:43

1 Answers1

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Without any additional information, all we can conclude is that

$$n\ge0$$

where $n$ denotes the number of students. You can't have a negative number of people. If you want my philosophical take on it, I would say that $n=0$ because remote learning was started as a response to COVID-19.

Lucien Jaccon
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