Example of median of continuous data?

Answer 1

a discrete probability distribution, a median m satisfies the inequalities

or

in which a Lebesgue-Stieltjes integral is used. For an absolutely continuous probability distribution with probability density function ƒ, we have

[edit]Medians of particular distributions

The medians of certain types of distributions can be easily calculated from their parameters:

• The median of a normal distribution with mean μ and variance σ2 is μ. In fact, for a normal distribution, mean = median = mode.
• The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean.
• The median of a Cauchy distribution with location parameter x0 and scale parameter y is x0, the location parameter.
• The median of an exponential distribution with rate parameter λ is the natural logarithm of 2 divided by the rate parameter: λ−1ln 2.
• The median of a Weibull distribution with shape parameter k and scale parameter λ is λ(ln 2)1/k.