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:
“No doubt, the short distance to which you can see in the woods, and the general twilight, would at length react on the inhabitants, and make them savages. The lakes also reveal the mountains, and give ample scope and range to our thought.”
—Henry David Thoreau (18171862)