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Genealogical averages

We all have simple ways to measure about our family trees. For example, we can count how many people appear in our family tree or how many direct ancestors we know about. We can boast about the date of our earliest ancestor or lament a more modern gap in our tree.

I am somebody who is interested in both mathematics and genealogy and I decided to play with some more interesting ways to measure a family tree. In particular, I wanted to be able to calculate the genealogical average of any quantity. Some examples of interesting numbers to calculate are the completeness of a family tree or the average date your ancestors came to your country (if your family is not native to its area, like most people from Australia or the USA).


Completeness

One important property of a family tree is its completeness. The two easiest ways to define the completeness of your family tree are:

  • count the number of people or direct ancestors it contains
  • count how many generations it goes back

These methods are fairly primitive though, so lets consider some better ones.

One thing I don’t like about these measures is that they become infinite as a tree approaches completeness. I would prefer a measure that approached 1 as a tree was completed so that you could define the completeness as a percentage. If we want that to happen then we’ll have to weight each generation so that the measure converges. The more mathematical details of all this are explained here.

I implemented my completeness measure in some computer code so that I was able to calculate these things for my own family tree¹. This measure defines my family tree to be 96.3% complete, while my parents family trees are 91.4% and 93.8% complete.


Genealogical average

This type of maths can be applied to define quantities that are more interesting than mere completeness. We can define the genealogical average of almost anything. One thing that was of interest to me, as someone born in an immigrant society like Australia, was to define the average year my ancestors immigrated to Australia.

In order to calculate the average year of immigration, the average will only be calculated over immigrants. The weighting factor will be \frac{1}{2^n} , corresponding to the ammount of blood shared with the ancestor. In my own family tree, I calculated the weighted average year of arrival in Australia is 1854.6. My parents averages are 1856.7 and 1852.5 and obviously mine is bang the middle of these two numbers. Once again, the details of these calculations can be found here.

Although I enjoyed programming all this myself it would be nice if something similar to a genealogical average were implemented in a common family tree program so that I could compare my numbers to some others!


¹ I had to write my own gedcom reader. Don’t get me started on the idiocy of the gedcom 5.5 standard!