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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

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problem

Problem

Would a restriction on height, such as prohibiting males from marrying taller females, affect the height of the entire population?

outline

Outline

Height Distribution

Means and Standard Deviations in U.S.

Other countries’ statistics

Affect of taboo

Setting parameters & Assumptions

R code

Problems

Adding the taboo

Some more problems

height distribution4

Height Distribution

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.

united states

United States

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

other countries

Other countries

Certain cultures discourage males from marrying taller females. This is especially true for arranged marriages.

India

Female: 5 ft 1 inch

Male: 5 ft 7 inches

Difference: 6 inches (greater than US)

Pakistan

Female: 5 ft 4 inches

Male: 5 ft 5 inches

Difference: 1 inch

Iran

Female: 5 ft 3 inches

Male: 5 ft 8 inches

Difference: 5 inches

Iraq

Female: 5 ft 1 inch

Male: 5 ft 5 inches

Difference 4 inches

trends

Trends?

There were no specific trends for these countries with regards to the taboo.

Reasons:

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.

parameters assumptions

Parameters & Assumptions

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

offspring calculation

Offspring calculation

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…

r code

R code

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.

problems

Problems

The assumptions made in the original parameters. (Offspring Calculation)

This method limits the amount of children per couple.

Height is dependent on other factors:

Nutrition

Medical history

Genetics

Environment

Etc

inserting the taboo

Inserting the taboo

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?

more problems

More problems

There will still be people that disobey the restriction.

Males are generally taller than females.

Immigrants

Now, most women choose a man that is taller than they are.

Will this information interfere with comparing data?

next time

Next time

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.

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