It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end. Adding (a, b) to the above equation gives 2(a, b) - (x1, y1) = (x2, y2) Adding (x1, y1) then gives 2(a, b) = (x1, y1) + (x2, y2) Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2 The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2 midpoint = (4, 5)
The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.