# Sample Size + Population Size

Six Sigma – iSixSigma Forums Old Forums General Sample Size + Population Size

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• #51004

Sah
Member

Is Sample Size dependent on Population size? My basic level of academics reminds me that sample size is independent of population and also on the period of eveluation;
I need a good explanation behind this theory which validates that Sample size id independent of population size and period.

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#176117

Severino
Participant

Take a look at your formulas.  Does big ‘N’ (population size) appear in them or does it only include little ‘n’ (sample size)?

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#176118

Sah
Member

Agree that the formula does not include the population figure; what i am looking at is a valid answer as to why sample size should not be dependent on population size. the answer to be explanatory for someone who does not understand statistics

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#176120

Szentannai
Member

Hi Student,
I know this question puzzles almost everybody during SS trainings and I have a favorite example to illustrate it:
Imagine an iceberg with ten million penguins on it (think of “The March of the Penguins” movie), where you already know that all penguins have heights between 0,94 and 1,06 meters. with a stdev of 0,02 m. How many samples do you need to measure the average height with a precision of say +/- 5 cms?
Not very many, right? Still, it is a huge crowd of penguins …
So, the point is, if the variation inside the population is small, you can get a good measurement of the average with a few samples. If the variation is large, you need many samples to capture it even if the population is relatively smaller.
P.S. Be careful with the example if you use it. It brought me the nickname “the penguin” at one large company :)
Regards
Sandor

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#176158

Darth
Participant

Student,
And now for the correct answer. It depends. If the population is large, then the sample size is not affected by the population. Where you have a small population relative to the calculated sample size then yes, the sample size depends on the population size. In that circumstance you use the finite population correction factor to revise the sample size down. General rule is that if the calculated sample size is greater than 5% of the population use the correction factor. Do a little research to get the actual formula.

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