It is the difference between the upper and lower quartiles; hence, it does not include extreme values present in the data. To calculate IQR, first, the data should be arranged in ascending order. Now the lower quartile can be found at the position (n + 1)/4, and the upper quartile at the position 3(n + 1)/4 in the data. The idea is that we wish to be a quarter and 3 quarters on the way through the data to find the lower and upper quartiles, respectively. The lower quartile (Q1) is the value under which 25% of data points are found, and the upper quartile (Q3) is the value under which 75% of data points are found, only when all the data points are arranged in increasing order.
If (n + 1)/4 is not an absolute value, then the lower quartile is calculated as
Value at the position (floor of (n + 1)/4) + (Value at the position (ceiling of (n + 1)/4) - Value at the position (floor of (n + 1)/4)) * fractional part of (n + 1)/4