# Interquartile range: Why add 1 to the sample size

#### FluffyStats

##### New Member
My understanding is that the interquartile range is calculated by taking the difference between the (N+1)*0.75th observation and the (N+1)*0.25th observation. For example, with 7 observations, one would take the difference between observations 6 and 2.

My question is this: Why do we add 1 to the sample size in this calculation? This isn't done when taking the median, so I'm wondering why it's done when taking percentiles.

Even in your case, you do not guarantee $$n + 1$$ is divisible by $$4$$;