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?

Here is an example. Say there are 2001 students, and 1000 of them have a score of 0 and 1001 of them have a score of 100. Then the mean is around 50, but the median is 100, and there are no outliers in this dataset.
