**10 ** Nov

# Estimate how many fishes can fit in a pond (Analytics Interview Question) – Answer

Ivy Nov 10, 2013 2 Comments

How can you estimate the population of fishes in a pond? (recently asked in an analytics job interview).

It’s a classic estimation problem. There is a popular sampling method called capture – recapture or ‘Lincoln Index’ or ‘Pieterson’s Method’ which is used to estimate the size of an animal or human population. There are two versions of this method; we’ll discuss the simpler version (for the more complex version, please refer to this article). The method goes like this:

- You first capture say 100 fishes (
**c** ) from the pond. You tag or colour them and return to the pond. So, if the total number of fishes in the pond is say ( **N** ), then the proportion of coloured fishes to the population is **c / N**.
- Now, again you fish and recapture a sample of say 100 fishes (
**r** ) from the pond. Out of which, say 10 ( **t** ) fishes are the coloured fishes that you had coloured or tagged in the first capture.
- Now, the proportion of the tagged fishes to the recaptured sample size is
**t/r** (10 / 100 = 10%). This, tagged to recapture sample (**t/r**), proportion is considered equal to the original population propertion (**c/N**).
- Hence,
**c / N = t / r . Or, N **(i.e., total population of fishes)** = (c x r)/t**
**Thus, the total fishes, in this case, would be : N = (100 x 100)/10 = 1000 fishes**

Do you agree or not agree or have any other method to suggest? **Please leave a comment below.** I’d be more than happy to discuss. Are you interested in more such analytics interview questions, **like our Facebook page** and automatically get updates on popular analytics questions and their indicative answers.

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Here you are supposing the numbers.How can you have the numbers for sure?Like in this case it is 100.It could be some other figure as well.That is why I feel that it cannot be generalised.

Hi Nilanjana, the numbers are just illustrative in nature to explain the approach. You could explain in terms of pure variables as well. The approach is the key here.