Interquartile Range Calculator

The IQR is the spread of the middle 50% of your data. It is the distance between the first quartile (Q1, the 25th percentile) and the third quartile (Q3, the 75th percentile). A small IQR means the middle half of your values is tightly packed; a large IQR means the middle half is spread out. Because it ignores the bottom 25% and top 25%, it tells you about the typical bulk of the data rather than its extremes.

This calculator uses the exclusive (Tukey) method: sort the data, find the median, then for an odd-sized dataset exclude the median from both halves before taking each half's median for Q1 and Q3. The inclusive method (used by Excel's QUARTILE.INC and many textbooks) includes the median in both halves for odd-sized data, which pulls Q1 and Q3 slightly toward the center. For even-sized datasets the two methods agree. Tukey's exclusive method is the original convention from John Tukey's exploratory data analysis work and is what most boxplot tools use.

The IQR depends on the middle ranks rather than the magnitude of every observation, so isolated extremes usually affect it far less than they affect the range or standard deviation. In small samples or after rank positions change, an endpoint can still influence Q1 or Q3 under the selected quartile method. Robust does not mean completely unchanged.

Tukey's fences flag values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. With Q1 = 2, Q3 = 5, and IQR = 3, the fences are -2.5 and 9.5. The multiplier is a convention, not a probability threshold. For a normal distribution, about 0.7% of values fall beyond the two fences combined, roughly 0.35% in each tail.

Use the IQR when your data is skewed, has outliers, or comes from an unknown distribution; it gives an honest picture of the middle 50% without being inflated by extreme values. Standard deviation is the right choice when your data is roughly symmetric and outlier-free (often assumed for normal distributions) because it uses every observation and pairs naturally with the mean. Quick rule: if you would report the median as your center, report the IQR as your spread; if you would report the mean, report the standard deviation.