What is the average length of the base of the nose (the tip i guess) in a female?

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The desired size of a nose in length or width cannot be measured in absolute numbers. The length, width, and projection of the nose in its entirety and its separate components are better measured in proportions to each other and surrounding facial features. There are ideal norms for these proportions but none of this is more important than stepping back, and looking at an individual and having a sense for what is pleasing to the eye. 

There really is no good way to give absolute measurements in mm for a particular nose characteristic. The goal of most rhinoplasties is to make the nose in harmony with the rest of the face, and to not be a distraction from the eyes, which are the center of human interaction. There are many guidelines for nasal aesthetics that are more in relation to other landmarks. For example, in Caucasians, the distance between the points where the nostrils attach to the face should be the same as the distance between the inner corners of the eyes. On profile, the angle the base of the nose makes with the upper lip should be about 95-110 degrees in women. Even that angle depends on the height of a woman, with taller women needing less angulation (so shorter people can't "look into their nose") and shorter women tolerating a more upturned nose. So, there are many guidelines but they aren't averages per se, more in relation to the rest of the patient's face.

The nose can be measured using many variables and ratios comparing length of dorsal line to tip projection to name one. These "standards" were based upon classic measurements in greco-roman figures.  Obviously this does not mean much to the billions of people not of this origin!

There is actually no average length which can be measured in numbers because what we always consider is aesthetic proportions. Ideally, length from the tip to the base of the columella should be equal to the vertical length of your upper lip (the distance between the base of your columella to your upper vermillion border.