Mean
Drag the red data points to see the computed values change. The data mean is shown in the dashed vertical orange line. The sum of squared difference with all the data points are plotted in yellow. Takeaway: the mean is the value which minimizes the sum of squared differences to all points.
Median
Drag the red data points to see the computed values change. The data median is shown in orange area. The sum of absolute differences with all the data points are plotted in yellow. Takeaway: the medians are the range of values which minimize the sum of absolute differences to all points.