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Chapter 2: Q 30. (page 108)

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

Short Answer

Expert verified

The mean and median are equal to 0.5

Step by step solution

01

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 0and 1

02

Step 2. Concept

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

03

Step 3. Calculation 

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

渭=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:

Md=arealiestotheleft=arealiestotherightMd=0.5

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

Therefore both the mean and median are equal to 0.5

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