IQR Calculator — Interquartile Range

The interquartile range (IQR) represents the difference between the upper quartile (Q3) and the lower quartile (Q1) in a ranked data set. Mathematically, the formula is expressed as IQR = Q3 - Q1. To find these values, the calculator first sorts your numerical inputs in ascending order. It then identifies the median (Q2) of the dataset. The median of the lower half of the data establishes the first quartile (Q1), while the median of the upper half establishes the third quartile (Q3). Subtracting Q1 from Q3 yields the final interquartile range, effectively neutralizing the skewing effects of statistical outliers.

Consider a dataset representing test scores from a mathematics quiz: 12, 15, 18, 22, 25, 27, 30, 32, 35, 40, and 45. First, we arrange the eleven numbers in ascending order, which they already are. The median of this dataset is the middle value, 27 (Q2). Next, we look at the lower half of the data below 27: 12, 15, 18, 22, and 25. The median of this lower subset is 18, making Q1 equal to 18. Then, we examine the upper half of the data above 27: 30, 32, 35, 40, and 45. The median of this upper subset is 35, making Q3 equal to 35. Finally, applying the IQR formula, we subtract Q1 from Q3: 35 - 18 = 17. Thus, the interquartile range for these test scores is 17.

When working with statistical distributions, always check your dataset for accidental duplicate entries or mistyped digits before running the calculation, as a single typographical error can significantly distort Q1 and Q3. Additionally, remember that while standard deviation is sensitive to extreme anomalies, the IQR is specifically chosen for skewed datasets because it remains robust against severe outliers.