Timeline for Variance of the median

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Nov 22 '21 at 4:37 answer BruceET timeline score: 0
S Nov 21 '21 at 16:49 history suggested Archana David CC BY-SA 4.0
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Nov 21 '21 at 16:46 comment added whuber stats.stackexchange.com/questions/45124
Nov 21 '21 at 16:24 comment added Sextus Empiricus Here you see that (as Laplace derived) the variance will be $\frac{1}{4nf(m)^2}$. The distribution density pops up because it relates to the derivative of the quantile function. If you fill in the density of a standard normal distribution then you get your result. (So your example counts as the sample median for a sample taken from a normal distributed population).
Nov 21 '21 at 16:18 comment added Sextus Empiricus The distribution of the median is like a beta distributed variable transformed by the quantile function. For increasing $n$ the beta distribution approaches a normal distribution with decreasing standard deviation. Then you can apply the Delta method to describe the distribution of the median.
Nov 21 '21 at 16:01 review Suggested edits
S Nov 21 '21 at 16:49
Nov 21 '21 at 15:51 comment added Henry The sample mean has variance $\frac{\sigma^2}N$ (optimal for a sample from a normal distribution) and $\dfrac{\sigma^2/N}{\pi\sigma^2/(2N)} \approx 0.64$
S Nov 21 '21 at 15:42 review First questions
Nov 21 '21 at 16:20
S Nov 21 '21 at 15:42 history asked Adriano CC BY-SA 4.0