The methods for calculating confidence intervals for a population median
assume that our data come from an SRS and will
give trustworthy conclusions only if this condition is met.
These methods make no assumptions about the distribution your data comes from.
If the $t$-procedures cannot be trusted to estimate a population mean,
these procedures may be used to estimate a population median instead.
Each interval is "symmetric" about the sample median in that
the end points of the interval are the same number of points
above and below the sample median.