If I understand your post correctly, you do not have the original data. If that were the case, I would suggest you obtain a bootstrap estimate of the standard deviation of the median and other relevant percentiles. Absent resampling from the empirical distribution, I'm not sure what the "best" solution would be. 

Perhaps a solution could be to assume a particular probability distribution, let's say log-normal, and estimate the uncertainty of the median by simulating random draws. This can be done in R pretty simply:

require(distr)

#number of data points to draw from the log normal distribution

n.draws = 100

# shape parameters for log norm distribution

mean.log = 0

sd.log = 1

# specifiy which percentile to investigate

percentile = .5

# number of times to repeat the "experiment"

n.replicates = 10000

# estimate the standard deviation

asdf

If I understand your post correctly, you do not have the original data. If that were the case, I would suggest you obtain a bootstrap estimate of the standard deviation of the median and other relevant percentiles. Absent resampling from the empirical distribution, I'm not sure what the "best" solution would be. 

Perhaps a solution could be to assume a particular probability distribution, let's say log-normal, and estimate the uncertainty of the median by simulating random draws. This can be done in R pretty simply:

require(distr)

#number of data points to draw from the log normal distribution

n.draws = 100

# shape parameters for log norm distribution

mean.log = 0

sd.log = 1

# specifiy which percentile to investigate

percentile = .5

# number of times to repeat the "experiment"

n.replicates = 10000

# estimate the standard deviation

asdf

Have a method for estimate confidence interval for median... but this is no easy!

Bakardjiev

Shane provided a very good approach via simulation. I've done this several times when I had summary data provided in papers, but not the detail. Your data will obviously not look exactly like that you're trying to replicate, but it should be pretty close. The problem will likely be with the bin sizes, unless you happen to know the bandwidth originally chosen.

My data were fitted with stable distribution having exponent alpha 1.5 - 1.58. Simulation is necessary movement of Levi. I have an article, and will look and join in Researtsh gate.