guidance w/ statistical analysis of heights, body parts

A forensic scientist is investigating three separate possible murders. In all three, only a single body part has been found. In the first case, it is a femur bone measuring 43.2 cm; in the second, it is an arm measuring 72.3 cm; and in the third case, it is an index finger measuring 7.4 cm. As part of the identification process, the scientist wishes to establish the height of each person.

a. Your task is to conduct an appropriate statistical analysis in order to establish, as accurately as possible, the height of each of the three people.

b. Which of the three body parts gives the most accurate indication of height? Use your analysis to give an objective, empirical answer.

In the above, what do they mean by 'statistical analysis'? What do they mean by an empirical answer?

Take out a ruler and measure the length of your arm, index finger, femur and height. We will compare these to measurements of persons 1,2,3

We assume that the length of bones are related to height. In such a way that a person who is half as tall will half bones which are half as long and so on.

We introduce the following notation:
\(\displaystyle Y\) You
\(\displaystyle H(X)\): Height of person X
\(\displaystyle F(X)\): Length of the femur of person X
\(\displaystyle A(X)\): Length of the arm of person X
\(\displaystyle I(X)\): Length of the index finger of person X

We now have that (under our assumption of bones being proportionally related to height):

\(\displaystyle \frac{H(Y)}{H(1)}=\frac{F(Y)}{F(1)}\)

And therefore: \(\displaystyle H(1)=\frac{F(Y)}{F(1)H(Y)}\)

Similarily for the others.

This may not be the correct answer, but it is an answer...

and the most accurate information would come from the longest body part (arm)

I'm leaning toward the femur, since that actually contributes to height, unlike arms or fingers. On the other hand, DaVinci certainly explained that arms are related to height, but it takes two arms for the same contribution as one leg.

Fingers are pretty vague. Are all piano players tall? I think not. Do all basketball players have huge hands? No. Most, but not all.

tkhunny said:

I'm leaning toward the femur....

Click to expand...

The femur is typically used by anthropologists, though, lacking such, I'm sure approximations could be made using bones from the arm.

Eliz.

The way i reasoned for the arms was that, given the choice, I would always want to examine the most of the body i could in terms of bone length. I don't know much about biology, it could perhaps be that the femur is a horrible measure of one's height (as counter-intuitive as it sounds). But i do believe you when you say that anthropologists use legs. If given the choice between a leg and an arm I would choose the leg due to it being longer. If given the choice between an arm and a femur... id flip a coin lol.