Ronda McCoy
Math 1040-014
Term Project Fall 2012
Data Collection Involving Relativity in the Lengths of Hands and Arms of Human Subjects

Purpose of the study:
The purpose of this study was to discover if there was any relativity between the length of someone’s hand and the length of their arm. We wanted to know if long hands meant that you had long arms, or if short and stubby hands meant that short arms were predictable. Essentially, we wanted to know if hand length was related to arm length.
Study Design:
The study design included simple random sampling for residents in Salt Lake City. 15 women were measured for hand length and arm length, and 15 men were also measured inclusively. We each took a sewing measuring tape and used centimeters as the measurement. The hand was measured from the base of the wrist, centered and in line with the pisiform bone, to the tip of the middle index finger. The arm was measured from the point of the shoulder, at the top of the head of the humerus bone, down to the end of the middle index finger. It was important that the individuals that were measured were over the age of 18 because we wanted to ensure that the full growth and maturity of the bones of each individual were met and completed.
Data, Statistics, and Graphs:
1. The data is as follows with regards to males and females and the lengths of their hands and arms. All data is organized into a table for convenience.
60
40
20
0
100
80
1 2
All Male Particapents
1:Hand Length Measurements
2: Arm Length Measurements
Ряд8
Ряд9
Ряд10
Ряд11
Ряд12
Ряд13
Ряд14
Ряд15
Ряд1
Ряд2
Ряд3
Ряд4
Ряд5
Ряд6
Ряд7

100
80
60
40
20
0
1 2
All Female Participants
1: Hand Length Measurements
2: Arm Lengh Measurements
Ряд9
Ряд10
Ряд11
Ряд12
Ряд13
Ряд14
Ряд15
Ряд1
Ряд2
Ряд3
Ряд4
Ряд5
Ряд6
Ряд7
Ряд8
2. The statistics for our first quantitative variable, which was the measurements of the hands, were as follows: the mean, or average, of the all of the measured hands was 18.453 cm with a standard deviation of 18.4 cm. The range of data for the hands was between 13 cm and 22.3 cm, and the five number summary included a minimum of 13 cm, the quartile one was 17.5 cm, the median, or middle, was 18.4 cm, and the maximum was 22.3. The most common hand length that occurred four times out of thirty, or the mode, was 17.8 cm, and there was only one outlier at 13 cm.
3. The frequency histogram for our first quantitative variable, or the measurements of all the hands in centimeters, is included. Notice that most of the hand lengths were between 16 and 18 centimeters.

4. In reference to the five number summary, we drew a boxplot for all of the hands that we measured, or our first quantitative variable.
5. The second quantitative variable that we compared the hand lengths to was the arm lengths of the same individual measured in centimeters (cm): The mean of all the arm lengths was 73.44 cm with a standard deviation of 5.914. The range between all the data was 63.5 cm and 83.8 cm. This information allowed us to gather the five number summary which included a minimum of 63.5 cm, the first quartile was 68.3 cm, and middle, or median, was 73 cm, the third quartile was 78.6 cm, and the maximum was
83.8 cm. There were two most common occurring lengths, or the modes, within all the participants which were 63.5 cm and 79 cm each occurring twice. In this data set, there were not any outliers.
6. The frequency histogram for our second quantitative variable, which was the measurements of all the arm lengths of one arm form each individual is included.

7. In reference to the five number summary given for the second quantitative variable, we constructed a boxplot for all of the arm lengths. The boxplot is included.
8. We conducted statistics for testing the correlation between two variables: linear correlation coefficient (R) and equation for line of regression; The linear coefficient for the two variables was y=1.78x+41.032, comparatively. The linear coefficient (R) is 0.55091;
9. The following data includes a scatterplot that includes all of the data with the line of regression.

90
80
70
60
50
40
30
20
10
0
0 y = 1.5347x + 45.119
Ряд1
Линейная (Ряд1)
5 10 15
20 25
Difficulties or Surprises:
Since we did a simple random sample, it was very easy to collect the data; however, the exact placements for measurement might have been inconsistent. When we measured it may not have been clear as to the right places to measure from. Also genetics play a factor in height and length of extremities which was not taken into consideration for this data collection series. Including a larger data set with regards to height might also help with the validity and overall comprehension of the comparison between hand and arm length. In addition, it would be wise to collect genetic history information from each individual to find out the heights of their relatives.
Analysis:
We found the differences between arm length and hand length and it ranged between 44.5 centimeters and 64.1 centimeters. The average difference was 54.986 cm, and it did not have any outliers, so each individual is very proportionate such that short arms seem to have shorter hands. However, long arms don’t necessarily mean that the hands will be long as well. The one outlier for the hand length was for an adult woman with long arms, but she also had very stubby fingers. This might be due to a genetic factor. It seems that there could be an equation made to estimate the difference between the length of a person’s hand and arm, but more information would be required.
Interpretation and conclusion:
In conclusion to the study, it is safe to say that generally long arms mean one will have long hands; and short hands, might mean one will have short arms. However, there is evidence that short hands could be linked with people with long arms, this is could all be linked to genetics.