Continuous random upper quartile

Remember that the lower quartile of any distribution is the value where 75% of the data is below it and 25% of the data is above it.

When talking about probability and distributions, the upper quartile is where the cumulative probability is 0.75.

Finding a formula

Knowing our formula for finding the probability of a continuous random variable, P(a \leq X \leq b) = \int_a^b f(x)\,dx, as well as that the upper quartile is where the probability is 0.75, we can find that:

\int_0^af(x)dx=0.75

We can use definite integration and find the value of a - that’s the upper quartile!

Question	Answer
Remember that the lower quartile of any distribution is the value where 75% of the data is below it and 25% of the data is above it.	True
When talking about probability and distributions, what is the upper quartile?	The value where the cumulative probability is 0.75.
What formula defines the probability of a continuous random variable between a and b?	P(a \leq X \leq b) = \int_a^b f(x)\,dx
How do you find the upper quartile a for a continuous random distribution?	By solving \int_0^a f(x)\,dx = 0.75 using definite integration.