Per capita income is data that is collected quantitatively. Pre capita income is used to measure the average income received buy each individual in a given location in a certain year. It is derived by dividing a country’s or an area’s total income by its population. Therefore, it is data that is collected quantitatively because quantitative data is data that is expressed numerically ( Reid, 2013) . Per capote income is numerical data because it represents how much each person earns in a given geographical location in a given year. Since it is information about quantity and can be measured and expressed in number, per capita income is an example of quantitative data.
The range of the data is the difference between the uppermost and lowermost values in a data set ( Illowsky et al. 2017) .The data set of per capita income of the 20 richest countries is shown below:
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113,196.50; 83,716.80; 81, 151.9; 77, 795.4; 77,771.20; 69,687.60; 67,037.30; 65,111.60; 63,987.10; 59,795.30; 53,825.20; 52,367.90; 51,241.90; 50,022.60; 49,334.40; 48,868.70; 47,279.90; 46,564.00; 46,212.80; and 45,175.60. Source: World Bank.
In the per capita incomes of the 20 riches t countries based on 2019 data, the highest value is Luxembourg’s, while the lowest is Belgium’s. Thus, the data range = $113, 196.5 – $45, 175.6 = $68,020.9. The range of data for this set is large because it is even more than the lowest value. It means that Luxembourg’s per capita income is more than double Belgium’s. Therefore, the range of data demonstrate the difference in average income between Luxembourg and Belgium.
The mean refers to the average of a data set, while the median is the middle value of a data set. On the other hand, the mode is the most common value in a data set. The mean is derived by adding all the value and dividing by the number of items in the data set. Therefore, the mea of the per capita income data set = $1, 091, 196.40/20 = $60,662.02.
The median is derived by ordering the items in the data set from the lowest to the highest and finding the middle value ( Illowsky et al. 2017) . Therefore, it is the exact middle value. In the current data set, the middle value is between $59,795.30 and $53,825.20. Since there is no exact middle value, the media will be the average of the two value. Thus, the median = (59,795.30 + 53,825.20)/2 = $56, 810.25. There is no common number or value in the data set, therefore, the set has no mode.
The average of the data set is $60,662.02, while the median is $56, 810.25, which shows that they are close in value. When the mean and median are close in value, its shows that the data set has a symmetrical distribution. The data set has a symmetrical distribution because the middle number in the data set, when arranged from the lowest to the highest, is similar to the average, which is the balancing point in the data set ( Albers, 2017) .
The variance is the squared deviation of a variable from its mean. Therefore, it is the distance a set of numbers is spared out from its mean. The formula for standard deviation is:
S 2 = ∑ [(x i – x̅) 2 ]/n-1
x̅ is the sample mean, which is $60,662.02
S 2 = variance
X i = term in the data set
x̅ = sample mean
∑ = sum
n = sample size
n- 1 = 19
| X | x̅ | xi – x̅ | |
| X 1 | 113,196.50 | 52, 534. 48 | |
| X 2 | 83, 716.80 | 23, 054.78 | |
| X 3 | 81, 151.90 | 20, 489.88 | |
| X 4 | 77, 795.40 | 17, 133.38 | |
| X 5 | 77, 771.20 | 17, 109.18 | |
| X 6 | 69, 687.60 | 9, 025.58 | |
| X 7 | 67, 037.30 | 6, 375.28 | |
| X 8 | 65,111.60 | 4, 449.58 | |
| X 9 | 63, 987.10 | 3, 325.08 | |
| X 10 | 59, 795.30 | -886.72 | |
| X 11 | 53, 825.20 | -6, 836.32 | |
| X 12 | 52, 367.90 | -8, 294.12 | |
| X 13 | 51, 241. 90 | -9, 420.12 | |
| X 14 | 50, 022.60 | -10, 639.42 | |
| X 15 | 49, 334.40 | -11, 327.62 | |
| X 16 | 48, 868.70 | -11, 793. 32 | |
| X 17 | 47, 279.90 | -13, 382.12 | |
| X 18 | 46, 564.00 | -14, 098.02 | |
| X 19 | 46, 212.80 | -14, 449.22 | |
| X 20 | 45, 175.60 | -15, 486.42 | |
| ∑ = | $1,091,196.4 | $60,662.02 |
S 2 = 304970390.97
The standard deviation is the amount of dispersion or variation of a set of values. If the standard deviation is low, it shows that the value are closer to the mean. However, if it is higher, it shows that the values are spread over a larger area. The formula for standard deviation is:
√∑ [(xi – x̅) 2 ]/n-1
Therefore, the standard deviation is the square root of variance. In the case of per capita income, the standard deviation = √304970390.97 = 17,463. 4. Considering that the standard deviation is low, it means that the values in the data set are closer to the mean ( Albers, 2017) .
The mean per capita income is $60,662.02. Therefore, the countries that have a real per capita income that exceeds the average are 9. These are the countries whose earnings per individual are more than the average for the 20 countries.
The range of the data set is $68,020.9. The countries that have a per capita income greater than the range are 6. Therefore, the countries that are in the 10% part of the range = (10% x 6)/100% = 0.6 countries.
References
Albers, A. (2017). Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences . New York: John Wiley & Sons Inc.
Illowsky, B., Dean, S. L., & Illowsky, B. (2017). Introductory statistics . Houston, Texas: OpenStax
Reid, H. M. (2013). Introduction to statistics: Fundamental concepts and procedures of data analysis . Thousand Oaks: SAGE Publications.
World Bank. (2020). International Monetary Fund World Economic Outlook (October-2019). http://statisticstimes.com/economy/countries-by-gdp-capita.php
