In this tutorial I introduce you to how you calculate the median, lower and upper quartiles and percentiles for a continuous random variable.

Example

In this video I show you how to calculate the median and lower quartile from a probability density function (p.d.f) by way of a worked example.

Below is the example which you may like to try first as part of your maths revision and then check your methods with the worked solution.

The random variable X had a p.d.f. given by

f\left( x \right) = \left\{ \begin{array}{l} \frac{1}{{12}}\left( {5 - 2x} \right),{\rm{      }} - 1 \le x \le 2\\ 0,{\rm{                      otherwise}} \end{array} \right.

Find the median m, and the lower quartile Q1.