L4 Quantitative Methods

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L4 Quantitative Methods for Business Submitted By: Jasdeep Singh Module Leader: Dr Edward Anyaeji 1

Answer 1a: Country: As a qualitative variable, the variable "Country" represents the names of the countries included in the export dataset. Non-numeric qualitative variables, such "Australia," "Austria," and "Canada," classify the data according to unique nation names and offer crucial details regarding the export data's sources. Continent: "Continent" is a qualitative variable that indicates each country's association with a certain continent. This variable adds important contextual information to the export dataset by classifying nations according to their continental areas, including non-numeric categories such as "Oceania," "Europe," "North America," and "Asia." Time Period: The year and quarter that correspond to each export data point are indicated by the variable "Time Period". It belongs in the qualitative category as it consists of non-numeric categories like "Q1-2022," "Q2-2022," and so on. This variable gives the dataset a time dimension that makes it possible to analyze export trends across particular quarters and years. Value ($ millions): The export values for each nation for a certain time period are measured in millions of dollars by the variable "Value ($ millions)". Since it is a quantitative variable, mathematical operations may be performed on it because of its numerical measurements. The continuous values, which span a variety of numerical possibilities, represent the amount of money that exports are worth. This quantitative feature makes it possible to precisely analyze and compare export numbers throughout several quarters and between nations. Answer 2b: Country Mean Median Minimum Maximu m Standard Deviation Skewnes s Coefficient of Variation Canada 149,741 146,436 142,862 163,231 8,092.42 0.61 0.054 Chile 24,662 24,626 23,884 25,371 251.32 0.11 0.01 Colombia 15,209 15,333.50 13,764 16,391 1,069.55 -0.29 0.07 Costa Rica 4,075.25 4,079 3,901 4,258 146.08 0.25 0.036 Mexico 144,556.25 145,045 132,240 149,158 7,248.63 -0.36 0.05 United States 521,961.75 532,339 481,274 539,888 26,949.50 -0.11 0.052 Answer 2c: Skewness in the export data for North and South American countries reveals the distribution of quarterly values. It gauges the asymmetry, indicating if data is concentrated to the left or right of the mean. Positive skewness signifies a longer right tail, while negative skewness implies a longer left tail. This statistical measure provides valuable insights into the shape and tendencies of the export data distributions for these regions. 2

Different skewness levels are seen when export statistics for nations in North and South America are examined. A right-skewed distribution is suggested by Canada's positive skewness (0.61), which shows that the distribution is occasionally pulled to the right by higher export values. Chile's pattern is slightly skewed to the right, with a modest positive skewness of 0.111. Colombia, on the other hand, has a left-skewed distribution, as indicated by its negative skewness (-0.29), which occasionally suggests lower export values. The asymmetry of each nation's export data distribution is shown by these skewness values, which give important insights into the distinct economic trends and trade patterns of each nation. The export statistics from the US and Mexico show negative skewness (-0.36 and -0.11, respectively), indicating left-skewed distributions. This indicates that there are sporadic quarters with lower-than-average values, despite both nations' typically high export levels. Understanding the distributional subtleties and spotting any outliers in the export statistics for the US and Mexico depends on the analysis of skewness. This realization advances our knowledge of the variety and dynamism present in each of their distinct trade performances and economic environments. Answer 2: Distribution of Export Values Across Countries Export Value Frequency Relative Frequency 1 5 2.78% 2 66 36.67% 3 7 3.89% The export values are divided into three different categories in the table above, which shows the distribution of export values across the various countries: Low (1), Medium (2), and High (3). The number of nations in each category is shown in the frequency column. Interestingly, out of all the nations examined, 5 have poor export values, making about 2.78% of the total. This implies a group of countries having comparatively lower export levels. On the other hand, a considerable number of nations—exactly 66—fit into the Medium (2) export value group, accounting for 36.67% of the total. This suggests that countries with modest levels of export are present everywhere. In addition, seven nations—or 3.89% of the total—are included in the High (3) export value group. A normalized view is offered by the relative frequency column, which expresses the proportion of each export value category's member nations to all of the nations that were examined. This measure makes it easier to grasp the distribution in comparison by emphasizing the dominance of Medium (2) export values. Even though they are less common, the Low (1) and High (3) export value categories add to the total variety of the world economy. In order to support strategic decision-making and resource allocation, politicians, economists, and companies seeking insights into the disparities in economic activity and competitiveness among nations must have access to this distribution study. 3

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Answer 2b: Global Distribution of Export Values by Category 6% 85% 9% Frequency Low (1) Medium (2) High (3) This pie chart divides export values into three categories: Low (1), Medium (2), and High (3). It offers a thorough picture of the distribution of export values across different nations. Five nations are identified in the Low export value category, making up 2.78% of all the countries evaluated. These countries show a trend of comparatively lower export values, indicating possible opportunities for economic growth and increased competitiveness internationally. The majority of the nations, or exactly 66, comprise the Medium export value group, which makes up 36.67% of the total. This dominance suggests that countries with modest amounts of exports are widely dispersed, which is indicative of balanced economic performance. Lastly, 7 nations are listed in the High export value category, accounting for 3.89% of the total. These countries have a unique pattern of export values that are greater than usual, highlighting their economic strength and possible strategic positions in the international market. Answer 3a: Continent Average Exports ($ million) Oceania 229,785.00 Europe 468,663.10 North America 728,223.70 South America 79,192.50 Asia 358,967.30 The table "Average OECD member exports per continent ($ million)" is based on the provided data of OECD member countries' exports in 2022. Here's an explanation of each part of the table: Continent: The continents to which the OECD member nations in the dataset belong are listed in this column. Oceania, Europe, North America, South America, and Asia are the continents that are represented. 4

Average Exports ($ million): The computed average exports for each continent are shown in this column. Divide the total exports for each continent by the total number of times that continent appears in the "Continent" column to arrive at the computation. Oceania: In 2022, Oceania's (New Zealand and Australia) total exports will be $413,405 million. Because there are two Oceanian nations in the dataset, (413,405 / 2) = $229,785 million is the average. Europe: The total of all the listed European nations' exports in 2022 represents the exports for all of Europe. There are twenty-five European nations in the dataset. As a result, (Sum of European exports / 25) = $468,663.1 million is the average. North America: The total exports of the United States, Canada, Costa Rica, and Mexico in 2022 represent their combined exports. The average is computed as (Sum of North American exports / 4) = $728,223.7 million since the dataset contains four North American nations. South America: The combined exports of Chile and Colombia in 2022 represent the region's entire exports. The average is computed as (Sum of South American exports / 2) = $79,192.5 million since the dataset includes two South American nations. Asia: The sum of the exports from the Asian nations of Israel, Japan, Korea, and Turkey in 2022 represents their entire exports. The dataset contains four Asian nations, hence the average is (Sum of Asian exports / 4) = $358,967.3 million. Answer 3b: Oc ean ia Europe Nort h America Sout h America Asia 0.00 100,000.00 200,000.00 300,000.00 400,000.00 500,000.00 600,000.00 700,000.00 800,000.00 Average Exports ($ million) Average Exports ($ million) 5

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