Statistics: sample median, means, s.d. vs sample size

[jhson114]

i have a set containing 10000 data. i took 1000 samples of size 4, 16, 64, and 1024 and took the medians, means, and stadard deviations of each size. i graphed them sd of medians vs sample size, sd of mean vs sample size, and sd of s.d. vs sample size. for sample mean, i know from a textbook that:
SD of sample means = population SD / sqrt(sample size n).
But it seems from the graph i created using R, sd of medians and s.d. vs sample size all have the exact same looking graph, which to me suggests that:
SD of sample means, medians, and s.d. = population SD / sqrt(sample size n).
Is this right? it seems a little awkward. any input will be very helpful. thank you

 

[EnumaElish]

graph i created using R

What is R?

More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?

 

[jhson114]

R is just a program language kind of like matlab.

"More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?"

This is exact what I'm asking.