Interquartile Range of Distributions
The interquartile range of a continuous distribution can be calculated by integrating the probability density function (which yields the cumulative distribution function — any other means of calculating the CDF will also work). The lower quartile, Q1, is a number such that integral of the PDF from -∞ to Q1 equals 0.25, while the upper quartile, Q3, is such a number that the integral from -∞ to Q3 equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
where CDF−1 is the quantile function.
The interquartile range and median of some common distributions are shown below
| Distribution | Median | IQR |
|---|---|---|
| Normal | μ | 2 Φ−1(0.75) ≈ 1.349 |
| Laplace | μ | 2b ln(2) |
| Cauchy | μ |
Read more about this topic: Interquartile Range
Famous quotes containing the word range:
“Whereas children can learn from their interactions with their parents how to get along in one sort of social hierarchy—that of the family—it is from their interactions with peers that they can best learn how to survive among equals in a wide range of social situations.”
—Zick Rubin (20th century)