sum of all scores

3.14 The mean serves as the balance point for any distribution because the sum of all scores, expressed as positive and negative distances from the mean, always equals zero.

(a) Show that the mean possesses this property for the following set of scores: 3, 6, 2, 0, 4.

(b) Satisfy yourself that the mean identifies the only point that possesses this property. More specifically, select some other number, preferably a whole number (for convenience), and then find the sum of all scores in Part (a) expressed as positive or negative distances from the newly selected number. This sum should not equal zero.