Lab Assignment 1

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University of Alberta *

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161

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Statistics

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Apr 3, 2024

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COURSE: STAT 161 SECTION: R2 LAB #: 1 GROUP #: 45 GROUP LEADER: Aniket Jain GROUP MEMBER(S): Aniket Jain Cynthia Nguyen ______________________________ PLEASE FILL OUT THIS SECTION ONLY IF YOUR GROUP MEMBER(S) MISSED ANY OF THE DEADLINES: MEMBER(S) EXCLUDED FROM THIS LAB WHICH DEADLINE IS MISSED Kim Fundanera January 27 ______________________________ ______________________________ ______________________________ ______________________________ SUMMARY OF ISSUES (FURTHER EXPLANATION OF WHY THE ABOVE GROUP MEMBER(S) IS(ARE) EXCLUDED FROM THIS LAB REPORT): This member failed to contact our group and did not do any of the assignments.

Question 1: a) Count of INCOME Column Labels Row Labels Low Middle High Grand Total Africa 38 10 2 50 Asia 20 14 14 48 Europe 3 8 29 40 North America 5 10 9 24 Oceania 6 2 2 10 South America 1 8 5 14 Grand Total 73 52 61 186 The Gross National Income per capita (GNI) is high among 61 countries in the world while 73 countries are in the Low bracket. 52 countries reside in middle. Low-income Africa: (38/50) 100=76.00% Asia: (20/48)100=41.67% Europe: (3/40)100=7.50% North America: (5/24)100=20.83% Oceania: (6/10)100=60.00% South America: (1/14)100=7.14% From this data we can see that Africa has the highest percentage of low-income countries. Whereas, Europe and South America have the lowest percentage of low-income countries. High-income Africa: (2/50) 100=4.00% Asia: (14/48)100=29.17% Europe: (29/40)100=72.50% North America: (9/24)100=37.50% Oceania: (2/10)100=20.00% South America: (5/14)100=35.71% From this data we can see that Europe has the highest percentage of high-income countries. Africa, on the other hand, has the lowest percentage of high-income countries.

b) Answer the following questions based on your contingency table: I. What percentage of all countries are classified as low-income countries (have GNI values less than $4125)?  39.2473118% (73/186*100) ii. What percentage of all countries have GNI values of at least $4126?  60.7526882% (1-73/186*100) iii. What percentage of all countries are from North America and have GNI values above $12,735 (high GNI)?  4.8387097% (9/186*100) iv. What percentage of North American countries have GNI values above $12,735?  37.5% (9/24*100) v. What percentage of countries with GNI above $12,735 are from North America?  14.7540984 (9/61*100) c) The height of the bars represents income frequency of countries in each continent. Different bars depict level of Income i.e., Low, Medium, and High. 0 5 10 15 20 25 30 35 40 Africa Asia Europe North America Oceania South America Income Continents Frequency Bar chart of INCOME by CONTINENTS Low Middle High

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Question 2: a) Bins Frequency 0 0 12735 125 25470 27 38205 7 50940 13 63675 7 76410 2 89145 3 101880 1 114615 1 More 0 b)  Histogram is not symmetric.  The histogram is skewed to the right (positively skewed).  The histogram is unimodal  There are no outliers  61 countries have GNI above $25,470  The suitable measures of center and spread for the distribution are median and IQR. 0 20 40 60 80 100 120 140 0 12735 25470 38205 50940 63675 76410 89145 101880 114615 More Frequency GNI Histogram

Question 3: a) b) Africa’s distribution is skewed to the right, Asia is also skewed to the right, Europe is skewed to the right, North America is skewed to the right, Oceania is skewed to the right and South America is symmetric. Africa has 2 outliers, Asia has 3 outliers, North America has 3 outliers, Europe has no outliers, Oceania has 2 outliers and South America has none. Outliers for Africa → Seychelles and Libya Asia → Quatar, Macao, and Singapore North America → Bermuda, U .S and Canada Oceania → New Zealand, Australia  The Continent’s centers are all quite off center except for South America.  Rank (High to Low): Europe, North America, Asia, Oceania, South America, and Africa.

c)  Largest average GNI is of Europe (29756.72) and largest median GNI is of Europe (20410.62)  Smallest Average GNI is of Africa (2841.89) and smallest median GNI is of Africa (1416.14)  Smallest Spread of GNI Africa (3313.01).  Largest Spread of GNI Europe (39524.77).  Yes, the results confirm my conclusions about centres, Spreads and shapes reached in Part B.  Since there are 2 outliers in the given data for Oceania, we get a higher standard deviation than IQR and due to the presence of these 2 outliers IQR is the more accurate spread representation of data. Due to the existence of outliers, we may see a significant disparity between the SD and IQR of Oceania. Because standard deviation is impacted by the existence of outliers, it generates a bigger number than necessary and does not offer a reliable foundation for making inferences. However, since IQR is unaffected by the outliers in this situation, it can be a more useful tool for drawing conclusions. Africa Asia Europe North America Oceania South America Mean 2841.886008 15168.06152 29756.7248 17497.3967 13490.89792 11254.85018 Standard Error 465.4845924 2906.390467 3949.772022 4639.865271 6883.250033 1661.427845 Median 1416.137267 6130.934156 20410.61615 9466.779686 3516.732295 10688.78986 Mode #N/A #N/A #N/A #N/A #N/A #N/A Standard Deviation 3291.473118 20136.06382 24980.55166 22730.60478 21766.74781 6216.493768 Sample Variance 10833795.29 405461066.2 624027961.1 516680393.7 473791310.1 38644794.76 Kurtosis 3.013172323 2.485948868 0.899999647 7.176007869 3.27670867 0.415419521 Skewness 1.872938616 1.769425292 1.131883524 2.553696253 2.048019852 0.844884084 Range 13083.0401 80252.58723 101176.1164 98504.37142 62952.50092 22350.97552 Minimum 264.4238656 633.5347095 3382.042843 1410.951676 2196.653633 2834.955674 Maximum 13347.46396 80886.12194 104558.1592 99915.3231 65149.15455 25185.9312 Sum 142094.3004 728066.9532 1190268.992 419937.5208 134908.9792 157567.9025 Count 50 48 40 24 10 14 Q1 693.1685215 2023.567189 8230.14759 4414.549996 3089.128874 6027.578954 Q3 4006.182051 22804.49388 47754.9182 19103.40061 14178.74614 15160.52316 IQR 3313.01353 20780.92669 39524.77061 14688.85062 11089.61726 9132.944207

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Question 4: a) b) The scatter plot shows a positive correlation between life expectancy and wealth. It appears that life expectancy increases as wealth increases in a curved line. Life expectancy becomes over 80 years once the wealth is over $20,000. The data suggests that a $20,000 GNI can sustain an average life expectancy that can be seen in the 40,000 to 1,00,000 range. 0 10 20 30 40 50 60 70 80 90 0 20000 40000 60000 80000 100000 120000 GNI Life Expectancy GNI

Question 5: a) b)  Africa has the Highest Average and Median Birth Death Ratio hence possess the highest growth in population.  Europe has the lowest Average Birth-Death Ratio hence possess the lowest Population growth.  North America has the highest spread and Europe has the lowest spread.  Africa has two country outliers Mauritius and Seychelles one standing at 2.90 and one at 9.10 birth-death rate respectively.  Europe has one outlier country (Kosovo) standing at 10.40 birth death rate.

c) Africa Asia Europe North America Oceania South America Mean 24.91 13.73 0.704 9.79 17.99 10.61 Median 26.57 13.57 0.7 9.36 19.41 11.39 Standard Deviation 7.07 7.48 3.46 5.72 7.19 4.38 Variance 50.12 55.93 11.96 32.73 51.65 19.21 Q1 22.45 9.34 -1.9 4.87 13.93 7.85 Q3 28.76 18.41 2.65 14.82 22.55 13.63 IQR 6.32 9.07 4.55 9.96 8.616 5.779  Africa stands at the top in terms of birth-death ration with an average of 24.91.  Europe lies at the bottom in terms of birth-death ratio with an average of just 0.70.  Most of the countries have a low spread and hence values are closer to the mean values and does not give out many outliers except for the one in Europe and two in Africa.

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Lab Assignment 1

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