Central Limit Theorem: Fisheries Management

  • Context: High School 
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Discussion Overview

The discussion revolves around the Central Limit Theorem (CLT) and its application in fisheries management. Participants seek to clarify the theorem's definition and its relevance to sampling fish populations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests a general definition of the Central Limit Theorem, specifically in the context of fisheries management.
  • Another participant provides a mathematical formulation of the CLT, noting that under certain conditions, the standardized average of sampled fish ages approaches a normal distribution.
  • A different participant mentions a specific version of the theorem that applies when the sample size is greater than 30, indicating the use of the t-distribution for smaller samples.
  • There is a discussion about the implications of sample size on the approximation of the normal distribution, with one participant affirming that a larger sample size improves the approximation.
  • Another participant adds that as the sample size approaches infinity, the t-distribution converges to the normal distribution.

Areas of Agreement / Disagreement

Participants express varying interpretations of the Central Limit Theorem and its conditions, with no clear consensus on a single definition or application method in fisheries management.

Contextual Notes

Some assumptions regarding sample size and distribution characteristics are mentioned, but these are not fully resolved within the discussion.

Who May Find This Useful

Individuals interested in statistics, fisheries management, or the application of the Central Limit Theorem in practical scenarios may find this discussion relevant.

majin
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:rolleyes: just a query... does anyone have a general definition of the central limit theorom. I've been looking on the internet and all I've got is a whole lot of complex crap

P.S it would help if it was related to fisheries management
 
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simply put: under certain regularity conditions (finiteness of mean and variance), given Y_i are independent and identically distributed random variables.

\frac{\sqrt{n}}{\sigma}(\frac{1}{n}\sum_{i=1}^{n}Y_i-\mu) \rightarrow N(0,1)

You can think of the Y_i as fish that you are sampling from a population of fish who's mean age and variance you know. Then if you sample a large amount of fish. The average age of your sampled fish standardized as above will be approximately normal(0,1).
 
Last edited:
the one we were taught is that sqrt(n)(X-u)/(s) - >N(0,1) if s>30 otherwise you got to use the t distribution where s is the sample std deviation
 
ya so if your n is not large enough, the approximation is not comfortable enough to use the normal. that's fine.
 
yeh so as n->infinity the t distrubution tends to the normal
 

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