Quartile Deviation Calculator
Compute the quartile deviation (semi-interquartile range) and its coefficient from a data set — a robust, outlier-resistant measure of spread.
How it works
Q.D. = (Q₃ − Q₁) ÷ 2 · coefficient of Q.D. = (Q₃ − Q₁) ÷ (Q₃ + Q₁)
The quartile deviation, or semi-interquartile range, is half the distance between the first and third quartiles. Because it ignores the top and bottom 25% of the data, it is far less sensitive to outliers than the range or standard deviation. Its coefficient — the IQR divided by the sum of the quartiles — is unit-free, so you can compare the relative spread of data sets on different scales.
Worked example
For 12, 14, 15, 17, 21, 22, 24, 26, 28, 31 the quartiles are Q₁ ≈ 15.5, Q₃ ≈ 26.5. The IQR is 11, so the quartile deviation is 11 ÷ 2 = 5.5, and the coefficient is 11 ÷ 42 ≈ 0.262.
Sources: Interquartile range — Wikipedia
Frequently asked questions
How does quartile deviation relate to the IQR?
It is exactly half the interquartile range. The IQR measures the full spread of the middle 50% of the data; the quartile deviation reports that as an average distance on each side of the median.
When should I prefer it over the standard deviation?
Use the quartile deviation when your data has outliers or a skewed shape, because it only depends on the quartiles and ignores extreme values. The standard deviation is better for symmetric data where every observation should count.
What does the coefficient of quartile deviation tell me?
It expresses spread relative to the size of the values, so it is dimensionless. That makes it useful for comparing variability between two data sets measured in different units or with very different magnitudes.
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