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'.