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# MATH STUDIES IA

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#### Transcript of MATH STUDIES IA

Introduction Birth rate is a crucial global issue that exists today. The rate of births is a dominant factor in determining the rate of population growth in different countries. While some countries such as China seek to lower birth rate, others, like Italy and Korea, seek to increase it. Korea has one of the lowest birth rates in the entire world. Living here, I am surrounded by articles and advertisements that discuss the severity of the low birth rate and government efforts to relieve such problem, which is what led me to investigate this issue. Conclusion Interpretation Math Studies Mock IA

Judy Oh The relationship between birth rate and intelligence Data For this investigation, I will use the crude birth rate as the unit of measurement for birth rate. The crude birth rate is the number of births per 1,000 people in a year. Calculations Correlation coefficient There are many causes toward high or low birth rate, and I believe intelligence is one factor. My aim for this project is to investigate the relationship between birth rate and intelligence. My hypothesis is that birth rate and intelligence have a negative correlation. To validate this point, I will look at the average birth rates per country and the average IQ per country (as a measurement of intelligence) to find out if the correlation between the two factors are weak, medium, or strong. I will use the data collected by the CIA World Factbook, which gives the average annual number of births during a year per 1,000 persons in the population at midyear. The World Factbook collected data from 222 countries. 5% of 222 equals 11.1 (222 x 0.05 = 11.1), which rounds to 11, so the highest 5% I will use for this investigation would be rankings 1-11, the middle 5% would be 106-116, and the lowest 5% would be 212-222. For the calculations, I will use an estimated amount of countries. I will study the countries at the highest 5%, middle 5%, and lowest 5% of the rankings for birth rate. countries with the highest rate of birth (1-11) countries with medium rate of birth (106-116) countries with the lowest rate of birth (212-222) I will use Dr. Richard Lynn's calculations of the average national intelligence quotient (IQ) that he published in his book, IQ and the Wealth of Nations. mean/median/mode/range 1. Top 5% Mean: (47.60+46.60+45.80+43.20+43.10+42.12+40.58+40.42+40.09+39.36+39.34) / 11 = 42.564544 = 42.56 births/1000 people

Median: 42.12 births/1000 people

Mode: N/A

Range: 47.60 - 39.34 = 8.26 2. Middle 5%

Mean: 17.70+17.58+17.50+17.50+17.44+17.44+17.44+17.34+17.33+17.30+17.28 / 11 = 17.4409091 = 17.44

Median: 17.44

Mode: 17.44

Range: 17.70 - 17.28 = 0.42 Birth Rate IQ Mean: (69+74+84+68+79+68+69+69+76+68+64) / 11 = 71.63... = 72

Median: 69

Mode: 69

Range: 84 - 64 = 20 Birth rate 3. Bottom 5%

Birth rate Mean: (8.76+8.7+8.69+8.62+8.42+8.39+8.33+8.06+7.72+7.54+6.85) / 11 = 8.1890901

Median: 8.39

Mode: N/A

Range: 8.76 - 6.85 = 1.91 IQ Mean: (87+90+91+83+84+89+80+93+87+87+83) / 11 = 86.72... = 87

Median: 87

Mode: 87

Range: 93 - 80 = 13 IQ Mean: (96+104+100+98+106+105+99+98+108+107+100) / 11 = 101.90901 = 102

Median: 100

Mode: 100

Range: 108 - 96 = 12 I will use Pearson's correlation coefficient to find out if the correlation between birth rate and intelligence is positive or negative, and if it is strong, moderate, or weak. I will combine the 3 groups (top, medium, bottom) into one for this calculation. r = (covariance of X and Y) / [(standard deviation of X)(standard deviation of Y)] So then, how do I find out if the national average birth rate is affected by the national average intelligence quotient? 1. Find out the covariance:

= total of average birth rates in 3 groups

= 47.6+46.6+45.8+......+7.72+7.54+6.85 = 750.14 = total of average IQ scores in 3 groups

= 69+73+84+......+108+107+100 = 2863 = 59428.91 = 24104.9322 - 24104.93 = 254107 therefore... = (59428.91 / 33) - (average of x)(average of y)

= (59428.91 / 33) - (22.7315...)(86.7575...)

= (1800.876...) - 1972.131...

= -171.255... = -171.26 2. Standard deviation: Standard deviation of x: 14.85

Standard deviation of y: 13.37

14.85 x 13.37 = 198.54 3. Find r r = (covariance of X and Y) / [(standard deviation of X)(standard deviation of Y)]

r = -171.26 / 198.57

= -0.89 4. Correlation coefficient The correlation coefficient, r , describes the strength of association. For this data set, the correlation coefficient would be -0.89 , which is 0.79. This is a chart representing my calculations. I used the linear trendline function on Numbers (iWorks) to create a visual representation of the correlation. As you can see, there is a negative correlation between birth rate and intelligence. These results will be discussed in more depth in the conclusion. Validity One problem to this investigation is that intelligence cannot be exactly measured. Although the IQ test is one format of measuring intelligence/education, IQ does not directly translate to intelligence. However, for the sake of this investigation, I believe the average IQ test score is a fair numerical representation of a population's average intelligence. Countries with higher average IQ scores are more likely to have higher literacy rates and higher GDP, which can contribute to birth rate, typically in lowering it. Another limitation to this investigation is that I used an estimated amount to represent the average birth rates in different countries instead of doing the study on all 222 countries that are provided in the data collection. Thus, this decreases the reliability of my conclusion because only 15% of the total countries was taken into account. I tried to make the investigation more valid by separating the data into a high, medium, and low section, but other methods such as randomly selecting a few countries may have been more appropriate. Just by looking at the mean/median/mode of the three different groups studied, it can be seen that there is some sort of an inverse relationship between the average birth rate and average IQ score of a country, which supports my hypothesis. The countries that had the highest rate of births scored the lowest in the IQ tests (42.12 per 1000 people and a score of 72). The countries that were in the middle of the birth rate ranking also had the middle score for IQ (17.44 per 1000 and a score of 87). And finally, the countries that had the lowest rate of births score the highest in the IQ tests (8.39 per 1000 and a score of 102).

The correlation coefficient supports my hypothesis more accurately and mathematically. The following table included in the Mathematics for the International Student: Mathematical Studies text book shows the strength of an association according to the coefficient of determination (r-squared): According to the table a coefficient of determination value greater than or equal to 0.75 and less than 0.90 means that there is a strong correlation between the association. The r value that was derived from my calculations was 0.79, which means that there is a strong correlation between a nation's average birth rate and average IQ score.

The line of best fit in the chart below also shows a negative correlation between these two factors.

Therefore, it can be concluded that there is a strong negative correlation between a country's average birth rate and average IQ score. Basically, the higher the average birth rate of a country, it is more likely that the average IQ score would be lower. For instance, the range of the average birth rates was significantly higher in the "high birth rate" group, as compared to the other two groups, which showed a smaller difference between the highest and lowest values. Such aspects

should be considered because in the full CIA chart, the

middle to low birth rate groups ultimately

show little difference in the rate of births. WORKS CITED The CIA World Factbook. "Country Comparison: Birth Rate." https://www.cia.gov/library/publications/the-world-factbook/rankorder/2054rank.html?countryName=Haiti&countryCode=ha®ionCode=ca&rank=49#ha Richard Lynn. Intelligence and the Wealth and Poverty of Nations. "Table 4 - IQ for 185 Countries." http://www.rlynn.co.uk/pages/article_intelligence/t4.asp Coad, Mal, Glen Whiffen, John Owen, Robert Haese, Sandra Haese, and Mark Bruce. Mathematics for the International Student: Mathematical Studies SL for Use with IB Diploma Programme. Adelaide Airport, SA: Haese & Harris, 2010. Print.

Full transcriptJudy Oh The relationship between birth rate and intelligence Data For this investigation, I will use the crude birth rate as the unit of measurement for birth rate. The crude birth rate is the number of births per 1,000 people in a year. Calculations Correlation coefficient There are many causes toward high or low birth rate, and I believe intelligence is one factor. My aim for this project is to investigate the relationship between birth rate and intelligence. My hypothesis is that birth rate and intelligence have a negative correlation. To validate this point, I will look at the average birth rates per country and the average IQ per country (as a measurement of intelligence) to find out if the correlation between the two factors are weak, medium, or strong. I will use the data collected by the CIA World Factbook, which gives the average annual number of births during a year per 1,000 persons in the population at midyear. The World Factbook collected data from 222 countries. 5% of 222 equals 11.1 (222 x 0.05 = 11.1), which rounds to 11, so the highest 5% I will use for this investigation would be rankings 1-11, the middle 5% would be 106-116, and the lowest 5% would be 212-222. For the calculations, I will use an estimated amount of countries. I will study the countries at the highest 5%, middle 5%, and lowest 5% of the rankings for birth rate. countries with the highest rate of birth (1-11) countries with medium rate of birth (106-116) countries with the lowest rate of birth (212-222) I will use Dr. Richard Lynn's calculations of the average national intelligence quotient (IQ) that he published in his book, IQ and the Wealth of Nations. mean/median/mode/range 1. Top 5% Mean: (47.60+46.60+45.80+43.20+43.10+42.12+40.58+40.42+40.09+39.36+39.34) / 11 = 42.564544 = 42.56 births/1000 people

Median: 42.12 births/1000 people

Mode: N/A

Range: 47.60 - 39.34 = 8.26 2. Middle 5%

Mean: 17.70+17.58+17.50+17.50+17.44+17.44+17.44+17.34+17.33+17.30+17.28 / 11 = 17.4409091 = 17.44

Median: 17.44

Mode: 17.44

Range: 17.70 - 17.28 = 0.42 Birth Rate IQ Mean: (69+74+84+68+79+68+69+69+76+68+64) / 11 = 71.63... = 72

Median: 69

Mode: 69

Range: 84 - 64 = 20 Birth rate 3. Bottom 5%

Birth rate Mean: (8.76+8.7+8.69+8.62+8.42+8.39+8.33+8.06+7.72+7.54+6.85) / 11 = 8.1890901

Median: 8.39

Mode: N/A

Range: 8.76 - 6.85 = 1.91 IQ Mean: (87+90+91+83+84+89+80+93+87+87+83) / 11 = 86.72... = 87

Median: 87

Mode: 87

Range: 93 - 80 = 13 IQ Mean: (96+104+100+98+106+105+99+98+108+107+100) / 11 = 101.90901 = 102

Median: 100

Mode: 100

Range: 108 - 96 = 12 I will use Pearson's correlation coefficient to find out if the correlation between birth rate and intelligence is positive or negative, and if it is strong, moderate, or weak. I will combine the 3 groups (top, medium, bottom) into one for this calculation. r = (covariance of X and Y) / [(standard deviation of X)(standard deviation of Y)] So then, how do I find out if the national average birth rate is affected by the national average intelligence quotient? 1. Find out the covariance:

= total of average birth rates in 3 groups

= 47.6+46.6+45.8+......+7.72+7.54+6.85 = 750.14 = total of average IQ scores in 3 groups

= 69+73+84+......+108+107+100 = 2863 = 59428.91 = 24104.9322 - 24104.93 = 254107 therefore... = (59428.91 / 33) - (average of x)(average of y)

= (59428.91 / 33) - (22.7315...)(86.7575...)

= (1800.876...) - 1972.131...

= -171.255... = -171.26 2. Standard deviation: Standard deviation of x: 14.85

Standard deviation of y: 13.37

14.85 x 13.37 = 198.54 3. Find r r = (covariance of X and Y) / [(standard deviation of X)(standard deviation of Y)]

r = -171.26 / 198.57

= -0.89 4. Correlation coefficient The correlation coefficient, r , describes the strength of association. For this data set, the correlation coefficient would be -0.89 , which is 0.79. This is a chart representing my calculations. I used the linear trendline function on Numbers (iWorks) to create a visual representation of the correlation. As you can see, there is a negative correlation between birth rate and intelligence. These results will be discussed in more depth in the conclusion. Validity One problem to this investigation is that intelligence cannot be exactly measured. Although the IQ test is one format of measuring intelligence/education, IQ does not directly translate to intelligence. However, for the sake of this investigation, I believe the average IQ test score is a fair numerical representation of a population's average intelligence. Countries with higher average IQ scores are more likely to have higher literacy rates and higher GDP, which can contribute to birth rate, typically in lowering it. Another limitation to this investigation is that I used an estimated amount to represent the average birth rates in different countries instead of doing the study on all 222 countries that are provided in the data collection. Thus, this decreases the reliability of my conclusion because only 15% of the total countries was taken into account. I tried to make the investigation more valid by separating the data into a high, medium, and low section, but other methods such as randomly selecting a few countries may have been more appropriate. Just by looking at the mean/median/mode of the three different groups studied, it can be seen that there is some sort of an inverse relationship between the average birth rate and average IQ score of a country, which supports my hypothesis. The countries that had the highest rate of births scored the lowest in the IQ tests (42.12 per 1000 people and a score of 72). The countries that were in the middle of the birth rate ranking also had the middle score for IQ (17.44 per 1000 and a score of 87). And finally, the countries that had the lowest rate of births score the highest in the IQ tests (8.39 per 1000 and a score of 102).

The correlation coefficient supports my hypothesis more accurately and mathematically. The following table included in the Mathematics for the International Student: Mathematical Studies text book shows the strength of an association according to the coefficient of determination (r-squared): According to the table a coefficient of determination value greater than or equal to 0.75 and less than 0.90 means that there is a strong correlation between the association. The r value that was derived from my calculations was 0.79, which means that there is a strong correlation between a nation's average birth rate and average IQ score.

The line of best fit in the chart below also shows a negative correlation between these two factors.

Therefore, it can be concluded that there is a strong negative correlation between a country's average birth rate and average IQ score. Basically, the higher the average birth rate of a country, it is more likely that the average IQ score would be lower. For instance, the range of the average birth rates was significantly higher in the "high birth rate" group, as compared to the other two groups, which showed a smaller difference between the highest and lowest values. Such aspects

should be considered because in the full CIA chart, the

middle to low birth rate groups ultimately

show little difference in the rate of births. WORKS CITED The CIA World Factbook. "Country Comparison: Birth Rate." https://www.cia.gov/library/publications/the-world-factbook/rankorder/2054rank.html?countryName=Haiti&countryCode=ha®ionCode=ca&rank=49#ha Richard Lynn. Intelligence and the Wealth and Poverty of Nations. "Table 4 - IQ for 185 Countries." http://www.rlynn.co.uk/pages/article_intelligence/t4.asp Coad, Mal, Glen Whiffen, John Owen, Robert Haese, Sandra Haese, and Mark Bruce. Mathematics for the International Student: Mathematical Studies SL for Use with IB Diploma Programme. Adelaide Airport, SA: Haese & Harris, 2010. Print.