Height DistributioN. Alexa Curcio. Problem. Would a restriction on height, such as prohibiting males from marrying taller females, affect the height of the entire population?. Outline. Height Distribution Means and Standard Deviations in U.S. Other countries’ statistics Affect of taboo
Would a restriction on height, such as prohibiting males from marrying taller females, affect the height of the entire population?
Means and Standard Deviations in U.S.
Other countries’ statistics
Affect of taboo
Setting parameters & Assumptions
Adding the taboo
Some more problems
Males and females have different means, but the same standard deviation.
Separately, male and female height each follow a normal distribution.
While it may seem that adding both male and female heights to one graph would create a bimodal graph, this is not the case.
Average height for males: 69.2 inches:
5 ft 9.2 inches
Average height for females: 63.8
5 ft 3.8 inches
Standard Deviation for males & females is 2.8 inches.
Males are about 5 inches taller than females, both have the same standard deviation.
*Information taken from National Health and Nutrition Examination Survey
Certain cultures discourage males from marrying taller females. This is especially true for arranged marriages.
Female: 5 ft 1 inch
Male: 5 ft 7 inches
Difference: 6 inches (greater than US)
Female: 5 ft 4 inches
Male: 5 ft 5 inches
Difference: 1 inch
Female: 5 ft 3 inches
Male: 5 ft 8 inches
Difference: 5 inches
Female: 5 ft 1 inch
Male: 5 ft 5 inches
Difference 4 inches
There were no specific trends for these countries with regards to the taboo.
No specific law prohibiting a male from marrying a taller female.
Arranged marriages are part of a culture, not of the entire country. (Height is also dependent on regional and environmental factors)
Difficult to find data for height of a culture.
ie: Muslim heights (Middle East, Africa, Asia)
Data is inconclusive.
1. Difference in mean between male and female
2. Standard deviation for male and female
3. Height to assign to offspring
Female: average – 2.5 inches
Male: average + 2.5 inches
Or, make it more dependent on gender
(2/3father + 1/3mother)
4. What creates a stable distribution?
Have every pair have x children.
Record the mean and standard deviation of the new population
One formula for calculating male and female children based on parents height:
Female = (F+M)/2 -2.5
Male = (F+M)/2 +2.5
In order to calculate variance for sons and daughters, must assume the father and mother are independent.
The expected value is (F+M)/2 -2.5 or +2.5, and to find the variance, we find the variance of the expected value…
Create a generation of males and females that are standard normal.
Take a sample from this normal distribution, 1 male and 1 female.
Have these two mate and have 2 children, male and female.
Depending on whether the child is male or female, assign a height to the child.
Repeat this for approximately 100 generations.
Find the standard deviation and mean for males and females separately.
The assumptions made in the original parameters. (Offspring Calculation)
This method limits the amount of children per couple.
Height is dependent on other factors:
Construct R code which only allows males to marry females that are shorter.
To do this, insert the restriction within each while loop that will only accept male height greater than female height.
Look at this effect on the overall height distribution of the population.
If there is no significant difference, create a bigger constraint.
Will this create more or less diversity in height?
There will still be people that disobey the restriction.
Males are generally taller than females.
Now, most women choose a man that is taller than they are.
Will this information interfere with comparing data?
Take into consideration the other factors for the height. (More specifically, genetics)
Create a different taboo and see its effect.
Demonstrate the difference in standard deviations and means for males and females of different generations.