Averages. We all know what that means, conceptually. You add a group of numbers together and divide by the total of the numbers you added together. For example, 9 number locations that have a value of 10 each totals 90. If you divide 90 by the number of number locations, 9, you get 10 as the average. Of course, that’s a very simple example, but the concept applies no matter how many number locations or how big or small the numbers.
Often, we don’t grasp a good working knowledge of how to apply that math concept as it relates to our DNA results.
What I’m referring to here is the TIP calculator provided by Family Tree DNA, but this concept applies equally as well to any TMRCA (Time to Most Recent Common Ancestor) calculation, regardless of who is calculating it. The underpinnings, are, by necessity, the same.
At Family Tree DNA, the TIP calculator, the little orange button above, is available to you to compare Y-line results to matches and it will give you a rough idea of how long ago you can expect to have a common ancestor.
One of the most common questions I receive reads something like this:
“The TIP calculator says that we should be related at 99% within 12 generations, but my genealogy shows that it should be 8 generations. What is wrong?”
Or something like this: “The TIP calculator says we are related, but I have no idea how to interpret any of these numbers.”
The answer is that nothing is wrong and these are ranges of possibilities, based on average mutation rates of individual markers. Having said that, we know absolutely that mutations are random events. You can see this demonstrated in the Estes project where Abraham Estes (born 1647) who had 12 sons produced one line who has several people with no mutations as compared to Abraham, and another descendant whose line from another son has 8 mutations in the same timeframe. Now it’s obvious that both of these are on the outer bands of the spectrum, and the average is 4, which really is not reflective of either of these lines, but is dead center accurate for two of Abraham’s other sons’ lines.
Recently, I was working with the Nemaha Half-Breed Allottee, a list of names of mixed European/Native American individuals who received individual land allotments in 1860 in Nebraska from the government as a result of an 1830 treaty. When analyzing the 365 people who had European names, I realized that this is the perfect example of averages and how they do, and don’t, work. So let’s visit the Nemaha for a minute.
There are 122 different surnames represented, and the average then is that 2.99 people should carry each surname. 365 divided by 122=2.99. So let’s say 3 people, as it’s very close.
In reality, here’s how the surname distribution breaks down.
|Number of People Carrying Surname||Number of Surnames|
You can see that only 10 surnames actually have 3 people who carry them, for a total of 30 people, or about 12%. For the remainder, 90 surnames have fewer than 3 people, for a total of 25%, and 63% of the surnames have more than 3 people who carry that surname.
Stated a little differently, this average is accurate for 12% of the people, and inaccurate for 88%. It is close for many. About 23% fall directly on either side, meaning 2 people or 4 people carry that surname.
So what is the message here? Averaging tools, TIP included, do the best with what they have, which includes results at both ends of the spectrum. In this case, it includes the 54 surnames with only one person each, and the 3 surnames who each have over 10 people each, 11, 15 and 18, totaling 44 people. If these people were trying to make sense of these averages, 3 people per surname, these numbers would be totally irrelevant to them.
So the lesson here is to use these tools as a guideline, and nothing more. You could be in the middle and these tools could apply to your family exactly, or you could be in the family who has 18 people carrying one surname instead of the “average” of 3.
This reminds me very much of the ‘one size fits all” nightshirt that got passed around for some years at home when I was a kid. “One size fits all” really meant “fits no one” and translated into “no one was happy.” Of course, if you don’t understand the meaning of “one size fits all” and averages, you might be happy and think you have an answer that you don’t.