Extra Exercise 1 ---------------- (a) Only one (yellow) arrow is shown because the mean and median coincide. (b) When moving the rightmost point, the median is unaffected whereas the mean increases when the point is increasing in value. The median is unaffected because it is the middle observation of the three. The mean is affected by all 3 observations and be considerably affected by a single observation (and is therefore not resistant). When moving the rightmost point to the left, the mean gets close to and even smaller than the median. When moving the point across the second largest point, the median jumps from that point to the one now being second-largest. This is because with 3 points, the median equals the middle (or second largest) point. (c) With 5 (or another odd number) of distinct points, the median won't change when an extra point is added with its value being equal to the previous median value. This can be understood from the formula for the median for an even number of points, because the median equals the average of the two most central points (and in this case they are equal). Now adding an extra point does not change the median at all, no matter the value of this extra point. This is because regardless of where the new point is positioned, the new middle point will be one of the duplicate points at the previous median value.