I have worked this problem multiple times and am not sure I am doing it right

I took the beginning balance in common stock and the ending balance in common stock and added them then divided by 2. is this a weighted average and am I supposed to include the preferred stock? My teacher gave me this formula

Earnings per share=(net income-preferred dividends)/weighted-average common shares outstanding

Since it's a weighted-average of common shares outstanding, no you don't include preferred stock. Earnings per share is on common stock.

Averaging the beginning an ending balances isn't a weighted average. It's just a, uh, well regular old average.

To do a weighted average, you are "weighting" the amount of shares by how long you had them. This is true of any weighted average -- if there's more of one thing than another, it weights more in the average. In this case, you're weighting by time it exists.

For instance, if you had 100,000 shares for 5 months, then at the beginning of June you issued 10,000 more shares, then you would have 110,000 shares for 7 months.

So 100,000 x 5 months = 500,000
110,000 x 7 months = 770,000

Total 1,270,000 divided by the 12 months = 105,833 weighted average.

The average of 100,000 and 110,000 is 105,000. Notice your weighted average is a bit higher than that, because you have 110,000 shares for a longer period, so it weights a bit higher in the average.

Make sense?

(Just as an added note, sometimes problems will not have the necessary information to do something like this properly. If all you have available is the beginning & ending balances, then all you can do is average those two numbers.)