Question: A pension fund decides to invest $720 million in the shares of XYZ Inc., a company with a volatile share price. Rather than invest all the funds at once and so risk paying an unduly high price, it practises "dollar cost averaging" by investing $120 million per week in 6 successive weeks. The prices it pays are $50 per share in the first week, then $60, $45, $40, $75, and finally $80 in the sixth week.
(a) How many shares in total does it buy?
(b) Which is the most accurate statement of the average price: the arithmetic, the geometric, or the harmonic mean?