How Effective Is The Interaction Between Page and Its Fans On Facebook?

Facebook likes
We did a little research on how many likes you can get for each post organically on Facebook. We know that facebook has reduced organic visibility of the posts coming from pages. The number of views can vary between 3-30%. Facebook simply wants the page owners to boost their posts and pay. Smaller pages seem to have higher visibility than the large ones.

We have done a small research on how many likes can a single post get depending on the number of page fans. The graph is bellow. We picked a few big fan pages and checked 8-10 recent posts. Then we calculated the average value of the number of likes per posts. The ratio between the average number of post likes and the number of page fans is shown on the axis y.
Even though, the number of the selected pages is not high, the trend is quite clear. It is difficult to motivate people to like and share the posts coming from the fan pages. We overviewed a few busy pages of famous people, large companies and celebrities, and the stats do not differ from those on the graph.
FB stats graph

Big Facebook pages get little exposure

If you have much lower number of followers, e.g. 1,000 - 5,000, it might seem like your Facebook marketing has no impact, because you get only a very little likes/shares even though your posts are attractive/funny/entertaining.
We would like to leave this short article with an open end. How do you motivate your followers to share your posts? Are the stats of your page better than those in the graph?