Question

A uniform distribution What is the mean $\mu$ of the density curve pictured in Exercise $28$? What is the median?

Short answer

The mean and median are equal to $0.5$

Step-by-step solution

Step 1. Given

Over the range of $0$ to $1$, The curve maintains the same value $1$ and is $0$ outside the range of values. This signifies that the data described by this distribution has a uniformly distributed range of values between $0$and $1$

Step 2. Concept

The $p\%$ percentile of a distribution is the value having $p\%$ of the observations less than it.

Step 3. Calculation 

The rectangle's balancing point is the distribution's mean point. As a result, the mean is calculated as follows:

$\mu =1+0/2=0.5$

The median of a symmetric distribution is the point where the area of the curve is equal on both sides. As a result, the median is calculated as follows:

$$\begin{gathered} Md=arealiestotheleft=arealiestotheright \\ Md=0.5 \end{gathered}$$

The uniform distribution's mean and median are presented below.

Therefore both the mean and median are equal to $0.5$