Can someone explain this diagram showing the spectral type distribution of bright stars Can someone explain this diagram?

The text is in Dutch, free translation: "You are given a graph: a histogram of the 10 000 most apparent bright stars. Explain 1, 2 and 3."



The fact that the number of counted stars of types O and M is small due to 


O is bright but just very rare and,
M is common but quite dim.


The puzzling bit in this diagram is the sudden dip from a local maximum F (why is there a maximum) to G (why is G a local minimum). The drop from K to M is explained above - that being that M class stars are just very dim (is this all there is to say here?).

It seems that if there wasn't a dip at 3, and the graph would just continue, that the local max at K can be explained as being there just because there is a dip at G. If there wasn't a dip it wouldn't be a maximum and it'd just look like a bell-curve.

So 


Why is there a dip at G?
Why does it rise so smooth from O to F? Is it just because B - F are more common?
Why is there a maximum at F?
It's all to do with the relationships between mass, spectral-type and luminosity and the initial mass function of stars.

I think your explanation of points 1 and 2 are completely correct. O and B stars are rarely born and short-lived; so even though they have enormous luminosities relatively few make it into a list of stars ordered by apparent brightness. A further important reason is that although they are immensely luminous, the more distant examples that might have made it into the list, cannot make it into the list because they are in the Galactic plane (they are young and still close to where they were born) and thus severely affected by extinction.

M-dwarfs are indeed the most common type of star, but not common enough to overcome the fact that their luminosities are much, much lower than hotter stars.

The dip in G stars is actually a peak in the K-stars caused by giants. Most low(ish) mass stars will evolve towards more or less the same point in the HR diagram forming the red clump. These stars are luminous, older and not concentrated in the galactic plane, can therefore be seen to great distances and produce a peak in the number counts.

So you can see this using actual data rather than a cartoon, I producedthe HR diagram for the brightest 10,000 stars in the revised Hipparcos catalogue (about V&lt;6.7). You can clearly see the red clump of giants. Now collapse this distribution onto the B-V axis and you can see there is a local minimum at $0.6&lt;B-V&lt;0.8$ corresponding to G-stars.

Absolute colour-magnitude diagram for the brightest 10,000 stars


The corresponding B-V distribution for these stars. G-stars have $0.6&lt;B-V&lt;0.8$