Interquartile Range Calculator

Frequently Asked Questions

What is interquartile range (IQR)?

IQR = Q3 - Q1. Measures spread of middle 50% of data. Represents range where the central half of values lie. Robust measure not affected by outliers.

Why use IQR instead of range?

Range uses only min/max (affected by outliers). IQR shows where 50% of data clusters, ignoring extremes. Better for non-normal distributions.

How do I interpret IQR?

Small IQR: data tightly clustered. Large IQR: data spread out. IQR tells you if values vary greatly or stay close together in middle 50%.

How is IQR used in outlier detection?

Outlier fences: Q1 - 1.5×IQR (lower), Q3 + 1.5×IQR (upper). Values outside fences are potential outliers. IQR determines fence width.

What is the relationship between IQR and standard deviation?

IQR is nonparametric (no distribution assumption). Std dev assumes normality. For normal dist: IQR ≈ 1.35 × std dev.

Can IQR be zero?

Yes, if Q1 = Q3. Happens when 50% of data has identical values. Unusual but possible. Indicates no variation in middle.

How does IQR relate to median?

Median (Q2) is center. IQR surrounds median: Q1 to Q3. Median + IQR together show both center and spread of central data.

What quartile contains the IQR?

IQR spans from Q1 (25th percentile) to Q3 (75th percentile). Contains the second and third quarters of data (middle 50%).

How do I visualize IQR?

Box in box plot represents IQR. Box height = IQR value. Wider box = larger IQR = more spread. Narrower box = smaller IQR = less spread.

When is IQR most useful?

When data has outliers or non-normal distribution. IQR is resistant to extreme values, making it reliable for real-world messy data.