Lesson Stats

Pre Reading Questions Study the following:

Statistical breakdown For the 49 contested elections in which the heights of all the major-party candidates are known, the tallest candidate won 26 times (about 53% of the elections), a shorter candidate won 19 times (39%), and the winning candidate and tallest opponent were of the same height four times (8%). While the tallest candidate has won 19 of 28 elections since 1900, it should be noted that from 1789 up till and including the 1924 election, it was actually shorter candidates who had won more elections (15 wins for shorter candidates compared to 11 wins for the tallest candidates). It should be noted, however, that there have been three cases where the tallest candidate received more popular votes than the shorter, winning candidate but lost the election because their popular vote majority did not translate into an electoral college vote majority. This occurred in the 1876, 1888 and 2000 elections (the tallest candidate still did not receive the most votes in the other election where an opponent won more votes than the winner (1824)). This means that the tallest candidate has won the majority of popular votes 29 times (59%) and a shorter candidate has done this only 16 times (33%). These figures lend some support to the popular perception that the taller candidate prevails in presidential elections. The win-loss margin is far less than what has been suggested in the above-mentioned sources, however. Outcome Tallest candidate among the major parties wins A shorter candidate wins Winner and tallest opponent same height

Electoral vote winner Popular vote winner 53 percent of the time 59 percent of the time 39 percent of the time 33 percent of the time 8 percent of the time " "

What do you notice about the heights of most of the winners, compared to those of their opponents? Why do you think this might be? Does the appearance of the man also contribute to the success? Why? How about if the man is fat vs. if the man was slim? Why?

Post Reading Questions: a. Why might Francis Galton have believed that collecting measurements of British schoolchildren would help him breed “genetically superior human beings”? b. What is the author, Stephen S. Hall, implying when he says that it is “good news” that the class of genes found in fruit flies that can alter size and shape is found only in insects? c. What do Anne Case and Christina Paxson argue in their paper about the relationship between height and earning potential? d. How does a discussion of prenatal development, postnatal nutrition and family socioeconomic status complicate Case and Paxson´s findings? e. What is the difference between height and “growth potential in height”? f. What do you think is meant by the phrase “height premium” in this context? g. What do you think is meant by the phrase “human capital” in this context? h. What point is Hall trying to make with the examples of Vincent Van Gogh and Mahatma Gandhi? i. Do any of these studies prove a causal relationship between height and intelligence and/or success? j. Why does Dr. James M. Tanner say that “the most misleading term in the entire discussion may be ´on average’”?

Activity You will be put into two groups. Complete the quiz. Switch papers and correct the quizzes. Put the score up on top Put the class numbers into the following statistical representations. Mean Median Mode Range Variance Refer to the charts to figure out what each means and how to calculate the data. Further Questions for Discussion: -What is the difference between causation and correlation? -Is there any evidence that proves a causal relationship between height and intelligence or success? -What implications does the belief that there is a causal relationship between height and intelligence and success have on racism and sexism?

Success Is Relative, and Height Isn’t Everything By STEPHEN S. HALL

Tallness has always been viewed as a desirable physical trait — so desirable that more than a century ago, Francis Galton began collecting measurements of British schoolchildren as a prelude to his dream of breeding genetically superior human beings. Although his eugenics project went nowhere, his obsession with height survives in a word that has become part of every modern parent’s vocabulary: percentile. Galton both coined the term and developed the statistics that allowed percentiles to be plotted on a growth chart. Since physical size is such an intrinsic feature of basic (not to mention personal) biology, researchers have returned again and again to that fateful intersection of genes, environment and stature. When they throw human qualities like cognition or intelligence into the mix, the combination becomes both fascinating and dangerous, not least because of the half-baked lessons that sometimes make their way from the technical literature to dinner party conversations. A group of researchers at the University of California, San Diego recently reported, for example, that mutations in a class of genes dubbed Tweedle — as in Tweedledee and Tweedledum — can alter the overall shape of fruit flies; a mutated “TweedleD,” the scientists noted, produced “short and stout” flies. The good news is that this particular class of genes is found only in insects; the bad news is that it reinforces the Galtonian notion of size as a genetically determined trait that can possibly be manipulated. Such manipulation would look more socially attractive if the mere fact of being taller made a person smarter, as some research has suggested since the 1890s. The most recent researchers to venture fearlessly into the height wars are two well-respected economists at Princeton University. Last August, the economists, Anne Case and Christina Paxson, published a paper called “Stature and Status: Height, Ability, and Labor Market Outcomes” that is still reverberating. Economists have long been fascinated by data showing that tall adults tend to earn more money. Using data sets from four long-running studies conducted in the United States and Britain, Dr. Case and Dr. Paxson present evidence arguing that on average taller people earn more because they are, quite simply, smarter. They suggest that

the difference in cognitive ability becomes apparent as early as age 3. “Throughout childhood,” they write, “taller children perform significantly better on cognitive tests.” If this were as true as it sounds, the news would obviously provoke great consternation in any parent with a child smaller than average — a status that most of us, thanks to Galton and his percentiles, know by heart. But it turns out that the Princeton story is a bit more nuanced than that, and part of a very long debate. As Dr. Case and Dr. Paxson make clear in their paper, many studies have shown that height is not just a matter of genes, but has a lot to do with prenatal development, early postnatal nutrition, and even a family’s socioeconomic status. Indeed, the scientists who study human growth have known for almost two centuries that children who have ample early nutrition grow faster and taller than those raised in more deprived circumstances, and well-nourished children also have earlier growth spurts. Good “nurture” of this sort, including minimal exposure to disease, produces children more likely to reach their genetic potential in terms of height. And as the Princeton economists stress, “environmental factors that are thought to influence cognitive development” affect height. When you add it all up, it says something a little more complicated than “taller people earn more because they’re smarter.” Someone who is 6 feet tall, but might have been 6-foot-2 with better early nutrition, may not have developed as much cognitive ability as someone who was well-formed and well-fed all along but stands 5-foot-6. The more accurate, but much less catchy, formulation would be: all other things being equal, people who reach their growth potential in height, whether taller or smaller than average, are likelier to be smarter than those who don’t, probably because they benefited from optimal early development. “Part of what we are trying to do,” Dr. Paxson said, “is to focus on height as a way of getting people to focus on growth.” Dr. Case and Dr. Paxson offered their results as an alternative theory to a much-cited paper published two years ago by Nicola Persico and Andrew Postlewaite of the University of Pennsylvania and Dan Silverman of the University of Michigan. These researchers concluded that the “height premium” in an adult male’s income correlated most strongly with a boy’s height at age 16. They speculated that taller teenagers accrued “human capital” through athletic and social activities. Dr. Postlewaite said in an interview that he did not know how to reconcile the importance of adolescence in his earlier study to the more recent Princeton findings, where adolescence ceased to be a factor when childhood cognition was weighed. Perhaps the two studies do not require reconciliation, but rather illustrate how imperfect our grasp remains of a fundamental issue — growth and ability — that researchers have been struggling to understand for more than a century. Our measures of cognition remain tentative, and quantification of emotional or social intelligence does not enter into the formulations at all. While understandable, the economist’s focus on income as the key determinant of success reflects a narrow bandwidth of human value; in economic studies of this sort, penniless artists like Vincent Van Gogh or impoverished leaders like Mahatma Gandhi would be examples of bad labor market outcomes. The most misleading term in the entire discussion may be “on average”— a fact that Dr. James M. Tanner, the British growth researcher, pointed out 40 years ago. “Perhaps the best analogy is with accident statistics,” he said while delivering, of all things, the Galton Lecture to the Eugenics Society in London in 1966. “No one can tell if he will be killed in a motor accident next week, yet the total number of people who will be killed in this period can be predicted rather accurately. Equally the correlation we are discussing, like road deaths, tells us something of sociological but nothing of individual importance.” Dr. Tanner suggested then, as Dr. Case and Dr. Paxson did several months ago, that it might be useful to study how development in the womb and early childhood affects intelligence. It was a good idea 40 years ago, it’s a better idea today, and it would help shift the public conversation from relative height, which is burdened with social distraction, to optimal growth, which is about giving all children, small and tall, the best chance to reach their physical and intellectual potential. The mean, median, and mode are single numbers that help describe how the individual scores in a data set are distributed in value. A data set consists of the observations for some variable is referred to as raw data or ungrouped data. Calculating the Mean, Median, and Mode

The Mean The arithmetic mean is another name for the average of a set of scores. The mean can be found by dividing the sum of the scores by the number of scores. For example, the mean of 5, 8, 2, and 1 can be found by first adding up the numbers. 5 + 8 + 2 + 1 = 16. The mean is then found by taking this sum and dividing it by the number of scores. Our data set 5, 8, 2, and 1 has 4 different numbers, hence the mean is 16 ÷ 4 = 4. The Median The median of a set of data values is the middle value once the data set has been arranged in order of its values. To find the mean of 2, 9, and 1, first arrange in order: 1, 2, 9. The median is the middle number or 2. If you have an even number of values such as 1, 2, 5, and 8, the median is the average of the two middle numbers. The median for 1, 2, 6, and 8 is the average of 2 and 6 = 4. The Mode The mode of a set of data values is the number in the set that appears most frequently. For example, the number 5 appears three times in 1, 2, 5, 5, 5, 8, 8, 9. Since the number 5 appears the most times, it is the mode. A set of numbers that can have more than one mode, as long as the number appears more than once. In the data set 1, 2, 2, 3, 3, 4, 5. The mode is 2 and 3. We also can say that this data set is bimodal. If no number appears more than once, then the data set has no mode. Calculating the Range, Variance, and Standard Deviation

The Range Given a set of numbers, the range is equal to the maximum value in the data set minus the minimum value in the data set. The range tells you how spread the entire data is. For example, given the numbers -3, 5, -9, and 19. The highest number is 19. The smallest number is -3. The range is therefore 19 - (-3) = 22. Variance and Standard Deviation The variance and standard deviation of a data set measures the spread of the data about the mean of the data set. The variance of a sample of size n represented by s2 is given by: [The sum of (x - mean)2] s2 = (n-1) The standard deviation can be calculated by taking the square root of the variance.

Given the QUESTION, identify the ANSWER 1. The European countries of Hungary, Romania, Bulgaria and Greece are collectively known as the _______ states. Ο Balkan Ο Scandinavian Ο Iberian 2. The European countries of United Kingdom and Republic of Ireland together form _______. Ο British Isles Ο Great Britain Ο Iberian Peninsula 3. The European countries of Scotland, England and Wales are collectively called _______. Ο Great Britain Ο United Kingdom Ο British Isles 4. United Kingdom is made up of _______ and _______. Ο Great Britain, Northern Ireland Ο Great Britain, Republic of Ireland Ο Wales, Northern Ireland 5. The European countries of Spain and Portugal together form the _______ Peninsula. Ο Iberian Ο Scandinavian Ο Kola 6. _______ is the region of Europe that extends across the northern parts of Norway, Sweden, Finland and the Kola Peninsula of Russia. Ο Lapland Ο Benelux Ο Scandinavia 7. The European countries of Belgium, Netherlands and Luxembourg are collectively referred to as the _______ countries. Ο Low Ο Balkan Ο Nordic 8. The European countries of Norway, Sweden, Denmark, Finland and Iceland are collectively referred to as the _______ countries. Ο Nordic Ο Balkan Ο Iberian 9. The European island of Ireland has two divisions - _______ and _______. Ο Northern Ireland, Republic of Ireland Ο United Kingdom, Republic of Ireland Ο Northern Ireland, British Isles 10. _______ and _______ are the European countries that form the Scandinavian Peninsula. Ο Norway, Sweden Ο Norway, Denmark Ο Sweden, Denmark 11. The European countries of Norway, Sweden and Denmark are collectively called the _______ countries. Ο Scandinavian Ο Nordic Ο Balkan 12. West Germany and East Germany united to form Germany in 1990. Ο True

Ο False 13. The U.S.S.R. ceased to exist in 1991 and fifteen independant republics emerged. Ο True Ο False 14. Czechoslovakia collapsed and broke into two independant countries in 1993. Ο True Ο False 15. In 1991, Yugoslavia broke up into independant countries due to political conflict. Ο True Ο False 16. The European country of Netherlands is also known as Holland. Ο True Ο False 17. United Kingdom is the largest European country. Ο True Ο False 18. Turkey is the smallest European country. Ο True Ο False

1. Balkan The European countries of Hungary, Romania, Bulgaria and Greece are referred to as the Balkan states because they are lying in the Balkan Mountains. 2. British Isles The British Isles are made of the European countries of United Kingdom and Republic of Ireland. The British Isles are formed by 5000 islands, Ireland and Great Britain being the biggest of them. 3. Great Britain Great Britain is made up of the European countries of Scotland, England and Wales. 4. Great Britain, Northern Ireland Great Britain and Northern Ireland are collectively referred to as the United Kingdom. 5. Iberian

The Iberian Peninsula is made up of the European countries of Spain and Portugal. 6. Lapland Lapland is the region of Europe north of the Arctic Circle extending across the northern parts of Norway, Sweden, Finland and the Kola Peninsula of Russia. 7. Low The Low countries are Belgium, Netherlands and Luxembourg. They are so called because all of them are made up of lowlands. These three European countries are also called 'Benelux' countries. This is so because 'Be' stands for Belgium, 'ne' stands for Netherlands and 'lux' stands for Luxembourg. 8. Nordic The Nordic countries are Norway, Sweden, Denmark, Finland and Iceland. They are so called because all of them are united by certain economic factors. 9. Northern Ireland, Republic of Ireland The European island of Ireland has two divisions - Northern Ireland (northern part) and Republic of Ireland (southern part) 10. Norway, Sweden The European countries of Norway and Sweden make up the Scandinavian Peninsula. 11. Scandinavian The European countries of Norway, Sweden and Denmark are referred to as the Scandinavian countries. 12. True In 1990, West Germany and East Germany united to form Germany. 13. True In 1991, the U.S.S.R. ceased to exist and broke into fifteen independant republics. Of these, only seven of them are European republics today. They are Russia, Moldova, Ukraine, Belarus, Lithuania, Latvia, Estonia. 14. True In 1993, Czechoslovakia collapsed and broke into two independant countries of Czech Republic and Slovakia. 15. True Yugoslavia collapsed and broke into many independant countries in 1991 due to political conflict. 16. True Holland is another name for the European country of Netherlands. 17. False The largest European country is Russia. In fact, it is also the largest country in the world! 18. False The smallest European country is Vatican City. In fact, it is also the smallest country in the world!