Calculating Sample Size with Unknown Distribution and Given Statistics

[cdm1a23]

Hi everyone,

Quick question. If you have a given sample of unknown size, and unknown distribution, but you know the following:

1 - 90th percentile equals 10

2 - There are three observations that are 10 or greater

Is it correct to assume there are 30 observations in that sample?

Now what if I add the following data:

3 - The mean is 7

4 - The median is 6

5 - The standard deviation is 2

This was a question on our last test, and I was just curious about it.

Thanks!

 

[matt grime]

It depends on your precise definition of percentile. The initial assumption is not correct under one way of interpreting percentiles. There might be precisely 3 samples, for example. All of them equal to 10. Then all percentiles are equal to 10. Some might not allow that as an example, though. I'm not entirely sure what is 'correct'.

 

[tacman]

Hi,

The answer to your first question is no, it is not correct to assume there are 30 observations in the sample. The 90th percentile and the number of observations that are 10 or greater do not provide enough information to accurately determine the sample size. It is possible to have a smaller or larger sample size that still meets those criteria.

To calculate the sample size with unknown distribution and given statistics, you can use a formula called the "Rule of Three." This rule states that if you have the 90th percentile and the number of observations that are equal to or greater than a certain value, you can estimate the sample size by multiplying the number of observations by 3 and dividing by the 90th percentile.

So in your example, the estimated sample size would be (3*3)/10 = 0.9, which is not a whole number and therefore not a valid estimate.

Adding the additional data of mean, median, and standard deviation can help provide a more accurate estimate of the sample size. However, without knowing the distribution of the sample, it is still difficult to determine the exact sample size. The mean and median can give you an idea of the central tendency of the sample, but the standard deviation tells you how spread out the data is. Without knowing the shape of the distribution, it is hard to determine the sample size.

In summary, it is not correct to assume a sample size of 30 based on the given information, but using the Rule of Three and additional statistics can help provide a more accurate estimate. However, without knowing the distribution, it is still just an estimate and may not be completely accurate. I hope this helps clarify things for you.