What is the relationship between latitude and yearly average of daily sunlight?

The answer to your question is - none at all.

The addendum regarding climate and seasons adds several levels of complexity to the original question, as climate and seasons are effected by latitude. The seasons are reversed between the north and south hemispheres - July is mid-winter south of the Equator, while it is mid-summer in the North. The climate changes from one parallel to another as well, although air and ocean currents, and geography also have an effect.

The two answers above are, of course, correct. But that is if you consider the geometry of the sun's position using its center. Now, the sun has an apparent diameter of about half a degree. When do you consider the sun to be down, in other words; what is your definition of twilight?

According to the ICAO, the standard of aviation, the night - requiring night certification, navigation lights, etc - is defined as when the sun is six degrees under the horizon.

In France, for the ease of practice, it is said that an aircraft, not certified for night flight, can fly up to half an hour after sunset. But in Norway, where I live, we follow ICAO by the letter and say: six degrees. Why is that?

Well, the more north you go, the lower the sun is over the horizon and the less the angle with it, is. Here, the twilight is very long. So long that, a few years ago, we went flying through the night, at the summer solstice and assessed that, at 6,000 ft above the sea level, we were at all time with less than the sun six degrees under the horizon. That was in south Norway, at roughly latitude 60 north. In the north of Norway, we have the midnight sun.

So, depending on your definition of the length of the day, you could say that, the more north you go, the slightly longer the yearly average of daytime is.

hh