# Statistical Analysis of Correlation Between Height and Length of Body Parts

#### 110699

##### New member
I have a math assignment and I am having difficulties with the final question. I will show my progress below, but here is the question:

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.

This is my progress so far:
I have measured each of the body parts on my own body, and calculated at their ratio to my height. These were my results:
(cm)
Femur: 48.4
Arm length: 81.2
Finger: 8.1

I divided my height by each of these measurements to get a ratio for each of them, which were:
height/femur = 3.874
height/arm = 2.333
height/finger = 23.148

Should I obtain more data from other samples to find a more exact ratio between height and the individual body parts? With this, I could then calculate and establish the heights of the victims to solve part (a) of the question. In terms of the empirical answer in relation to what is the most accurate indication of height (part b), would I conduct a correlation coefficient to do so? Sorry if my progress so far is of little help, any replies would be appreciated. Thanks

#### mmm4444bot

##### Super Moderator
Staff member
Should I obtain more data from other samples to find a more exact ratio between height and the individual body parts?
Yes! You cannot do any analysis with only one data point. Also, these types of body measurements are very prone to errors (especially if you measure yourself).

Start with six samples (all adults), and then check the standard deviation for each body part. If any are too large (i.e., your data is really spread out), I would continue measuring.

Also, make sure that you're measuring correctly. A rigid device (like a yard stick) is better than a tape measure.

For the femur, the measurement ought to be done while the subject is sitting (thigh horizontal and back straight). You might be surprised to learn just how far into the pelvis the head of the femur goes. With the knees slightly spread, hold the yardstick against the inside of the thigh, and press it firmly into the crotch. Place another straight object on the patella (knee cap) such that it is perpendicular to the yardstick, and take the intersection point as the measurement.

For arm length, the subject's arm, hand, and fingers need to lie on a straight line (you're not a tailor). Again, press the yardstick firmly into the armpit and measure to the tip of the index finger.

If memory serves, from my healthcare days, on average (male and female), the adult femur is a little more than 26% of height. If your result in part (a) is reasonably close to that, then you're doing good.

In terms of the empirical answer in relation to what is the most accurate indication of height (part b), would I conduct a correlation coefficient to do so?
If by correlation coefficient, you're thinking of standard deviation divided by mean, then that sounds like a good plan.

Next, we both wait for tkhunny to weigh in (eg: how large is too large, for standard deviation), as it's been 20 years since I last studied statistics. :cool: