AS/A2 Stats 1 Stats 3

S2 Topic 2: Continuous random variables
Visualizing the quartiles
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 F(x) reaches 0.25. The value of x at this point is the 25th percentile or lower quartile, Q1, of the distribution. The value of x where the F(x) reaches 0.75 is the 75th percentile or upper quartile, Q3. Q2 is the 50th percentile, or median. The value of Q3- Q1 is called the interquartile range.

Answers The value required for a is about 0.00926. Q1 is about 1.4 and Q3 is about 3.3. 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