AS/A2 Stats 1 Stats 3

S2 Topic 2: Continuous random variables
Visualizing the median
The median, M, of a continuous distribution with pdf f(x) is the value that satisfies:
The following graph shows the pdf f(x) defined by:
a can be varied. Also shown is the cumulative probability function F(x) in red. This graph shows the total area under the pdf curve - ie., the total probability. First adjust a so that the total area under the pdf between 0 and 6 is 1. Then look to see where the cumulative probability function reaches 0.5. The value of x at this point is the median of the distribution.

Answers The value required for a is about 0.00926. The median, M, appears to be about 2.3. To find these values accurately you would need to use calculus. Based on free Java applets from JavaMath