Question

consider the given density curve. suppose that the mean value is 3.67. what is the best approximation for the median? 3.2 3.4 3.6 3.8

Explanation:

Step1: Recall property of symmetric distribution

For a symmetric distribution, the mean and median are equal.

Step2: Analyze the given density curve

The given density curve (a right - angled triangle with vertices at \(x = 1,x = 5,y = 0\) and \(y=\frac{1}{2}\)) is symmetric about the line \(x = 3\). But we are given a mean of \(3.67\). However, for a uniform - like (triangle in this case) distribution that is slightly skewed (but in the absence of full formulae, using the fact that for a non - highly skewed distribution, the median is close to the mean).
Since \(3.6\) is the closest value to \(3.67\) among the given options.

Answer:

\(3.6\)