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:
“We must continually remind students in the classroom that expression of different opinions and dissenting ideas affirms the intellectual process. We should forcefully explain that our role is not to teach them to think as we do but rather to teach them, by example, the importance of taking a stance that is rooted in rigorous engagement with the full range of ideas about a topic.”
—bell hooks (b. 1955)