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 the property of right - skewed and left - skewed density curves

For a right - skewed density curve, the mean is greater than the median. For a left - skewed density curve, the mean is less than the median. For a symmetric density curve, the mean is equal to the median.
This is a right - skewed density curve (since the tail is on the right side). So, the median is less than the mean.

Step2: Analyze the given options

Given the mean is \(3.67\).
We know that the median \(m\) satisfies \(m<3.67\).
Among the options \(3.2\), \(3.4\), \(3.6\), \(3.8\), the value \(3.6\) is the closest value to the mean that is less than the mean.

Answer:

\(3.6\)