How Is the PDF of the Sample Median Derived?

[natski]

I am familiar with the derivation of the probability density function of the sample mean but was looking for an equivalent derivation for the sample median. Does anyone know of a good, clear derivation of this PDF?

Thanks,

Natski

 

[statdad]

There are two situations. If the sample size is odd, then the median is the middle order statistic and you can immediately write down its pdf.

For the asymptotic normality result, you can look in books on probability or mathematical statistics. Bickel/Dobson have a text that is slightly higher level than Hogg/Craig. For a much more rigorous approach you can look at "Approximation Theorems of Mathematical Statistics" by Serfling.