why sample interquartile range distribution is a biased estimator of population interquartile range I'm curious, from experiments, i have found that sample interquartile range distribution is a biased estimator (i.e. underestimate) of the population interquartile range, but I can't seem to understand why this is the case from an intuitive sense. 
Also, how useful is of finding out the sample interquartile range?
 A: The question post isn't very specific so I'm gonna assume you're talking about (1) unbounded random variables (on half-real or the whole real line)  (2) not-so-advanced and not-so-complicated estimators for interquartile range.
The population quartiles take in contributions from every point all the way to the infinity (which ever direction(s) that is unbounded). Even though the density (if exists) becomes vanishingly small, all the points still count.
A sample of finite size cannot capture the tail all the way to infinity. 
There is always a chance to get some observations that are far out, but the distribution from the sample (histogram) is by definition truncated. 
When the sample size gets large, the data would become better and better (assuming proper sampling methods) in representing the population distribution. However, the tail behavior is not built-in as part of the raw data (e.g. histogram).
Unless you make adjustments to mathematically model the tail behavior, otherwise the simpler estimators for the quartiles don't get contribution from the faraway tail(s).
When it's unbounded in both direction, obviously both tails are lost in the estimator and the sample interquartile range is an underestimation.
When it's unbounded in only one direction, the corresponding "outside" quartile estimator is affected more by the loss of the tail, thus the sample interquartile range is still an underestimate.
