Say we have 6K to invest,for various reasons first we buy 3K of stock A than after some time we buy another 3K of the same stock,first time at 200 dollars and second time at 150.If one was supposed to calculate the average price of the stocks that we bought why do they have to use harmonic average and not the normal average we use ?

If you want to calculate it directly, figure out how many shares you bought each time and divide 6,000 by that total.

At 200/share, you bought 15 shares; at 150/share, you bought 20 shares. So 6,000/(15 + 20) = 171.43.

The harmonic mean of 200 and 150 is:

2 / (1/200 + 1/150) = 171.43.

Note that you can compute the answer as the weighted average of 200 and 150: the weight on each is the number of shares bought at that price (15 @ 200 and 20 @ 150).