Quartile deviation (also called semi-interquartile range) is half the interquartile range. It represents the average distance from the quartiles to the median.

Formula

Quartile Deviation = (Q3 - Q1) / 2
QD = IQR / 2

Interpretation

Quartile deviation shows how much the quartiles deviate from the median on average. Smaller values indicate data concentrated near the median.

Calculation Process

  1. Calculate Q1 (25th percentile)
  2. Calculate Q3 (75th percentile)
  3. Compute QD = (Q3 - Q1) / 2

Example: Q1 = 20, Q3 = 40 QD = (40 - 20) / 2 = 10

Advantages

✅ Robust to outliers ✅ Same units as original data ✅ Easy to interpret ✅ Useful for skewed data

When to Use

  • Describing data spread for skewed distributions
  • When outlier robustness is important
  • Quick assessment of data variability