Estimate the median from mean, variance etc.

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I'm given four groups containing 15 observations each. I can only see a few of the observations.

However, for each group, I'm given the variance, mean, sum, USS, SSD etc.

I have to estimate the median and specify a 95% confidence interval.

Of course, I think that if I could see all the 60 observations, I could just sort the numbers and calculate the average of the two values in the middle.

But how do I estimate the median given the above information? And specify a 95% confidence interval for it? What is the correct way to do it?

I have been searching a lot but I can't find a method to estimate it.

Help would be appreciated.