Why don't we automatically have outliers when mean and median differ strongly? Assume you have a data set with information on income of all students in the lecture. The mean value is 1500\$. The median value is however only 800\$. Which of the following conclusions is wrong?
The answer is: The difference between median and mean can be explained by outliers.
Why is this wrong? When Mean and Median deviate in such a manner, there have to be outliers or am I completely wrong? I can check outliers with |z| > 2.5 or a boxplot with IQR*1.5
But why do there not have to be outliers in such a case? I am completely lost and cannot think of a data set that fulfils such a case. Could you please help me?

The difference between the mean and the median is not a good sign of outliers.
Example: You have five students, four earning \$1 and the fifth earning \$6 dollars. Then, the median income is \$1 and the average income is \$2. In this example, the average is two times the median! But that doesn't imply we should exclude one student from our analysis.
