Data Analysis - Statistics Project Example

Data analysis June 17, Data analysis Different sources of data exist on s and even though data creates awareness and informs decisions, only reliable data should be used. This identifies need to verify data sources and consistency in data features between data sources is one of the approaches to establishing reliability of the two sources. Data on Gross Domestic Product (GDP) per capita for European Union countries is investigated to establish reliability between the World Bank and the Central Intelligence Agency (US) as information sources. Average GDP per capita (2013) of the European Union is computed from the World Bank data and is compared with data for individual countries as reported by the Central Intelligence Agency data (based on purchasing power parity). Data from the World Bank shows that the European Union had a GDP of $ 17.96 trillion and a population of 507.0 million in the year 2013. GDP per capita for the region can therefore be computed as follows (The World Bank, 2015). GDP per capita= 17.96 trillion/507 million= $ 35424.06 Hypothesis HO: µCIA= 35424.06; No significant difference between the two sources, sources are reliable HA: µCIA≠ 35424.06; A significant difference exist, one of the sources is not reliable µ represents mean The data are on a ratio scale and represents average output of a country per person per year. Data was collected through observation from existing sources, the World Bank and the Central Intelligence Agency (US), and with European Union countries as the population. The data is with respect to the year 2013 and may not represent the countries’ and the region’s current GDP per capita. The following table shows the data set for 25 European Union countries Table 1: Sample countries and their GDPs Country GDP per capita Country GDP per capita Country GDP per capita Austria 45100 Czech Republic 27800 Germany 44200 Belgium 41400 Denmark 43800 Greece 25500 Bulgaria 16800 Estonia 26500 Hungary 23600 Croatia 20600 Finland 40700 Ireland 45400 Cyprus 29200 France 40500 Italy 34700 Latvia 23200 Netherland 47200 Slovak Republic 27100 Lithuania 25800 Poland 23700 Spain 32500 Luxembourg 91900 Portugal 26100 Malta 31100 Romania 17700 (Central Intelligence Agency, n.d.) Statistics The following table shows the statistics, retrieved from Appendixes A, B, and C that are excel outputs. Table 2: Statistics Statistics Value Statistics Value Sample size 25 Mode 16800 Minimum value 16800 Mid range 54350{(minimum+ maximum)/2} Maximum value 91900 Range 75100 ∑x2 34614970000 Standard deviation 15237.008 Mean 34084 Variance 232166400 Median 29200 Q1 and Q3 14600 and 42600 respectively Graphs The following graphs describe the data. Graph 1: Frequency table GDPpercapita Frequency Percent Valid Percent Cumulative Percent Valid 16800.00 1 4.0 4.0 4.0 17700.00 1 4.0 4.0 8.0 20600.00 1 4.0 4.0 12.0 23200.00 1 4.0 4.0 16.0 23600.00 1 4.0 4.0 20.0 23700.00 1 4.0 4.0 24.0 25500.00 1 4.0 4.0 28.0 25800.00 1 4.0 4.0 32.0 26100.00 1 4.0 4.0 36.0 26500.00 1 4.0 4.0 40.0 27100.00 1 4.0 4.0 44.0 27800.00 1 4.0 4.0 48.0 29200.00 1 4.0 4.0 52.0 31100.00 1 4.0 4.0 56.0 32500.00 1 4.0 4.0 60.0 34700.00 1 4.0 4.0 64.0 40500.00 1 4.0 4.0 68.0 40700.00 1 4.0 4.0 72.0 41400.00 1 4.0 4.0 76.0 43800.00 1 4.0 4.0 80.0 44200.00 1 4.0 4.0 84.0 45100.00 1 4.0 4.0 88.0 45400.00 1 4.0 4.0 92.0 47200.00 1 4.0 4.0 96.0 91900.00 1 4.0 4.0 100.0 Total 25 100.0 100.0 Graph 2: Histogram Graph 3: Stem and leaf plot GDPpercapita Stem-and-Leaf Plot Frequency Stem & Leaf 2.00 1 . 67 4.00 2 . 0333 7.00 2 . 5566779 3.00 3 . 124 .00 3 . 5.00 4 . 00134 3.00 4 . 557 1.00 Extremes (>=91900) Stem width: 10000.00 Each leaf: 1 case(s) Graph 4: Box plot Hypothesis results The following table shows test of hypothesis results. One-Sample Test Test Value = 35424.06 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper GDPpercapita -.440 24 .664 -1340.06000 -7629.5876 4949.4676 The test is not significant (p=0.664> 0.05, t=-0.44). The null hypothesis is not rejected to the effect that mean of the sample is equal to the average GPD for the region. The two data sources are therefore consistent and identify reliability. Conclusion Distribution of the countries’ GDP per capita is skewed, positively, and has an outlier in GDP of Luxembourg that was $ 91900. The countries GDP per capita also differed widely as the high values of range ($ 75100) and standard deviation (15237) shows. High concentration of countries occurred in the second and fourth stems. Mean of the countries’ GDP per capita, based on CIA data (34084) is statistically the same as regional value that the Wwaorld Bank reported for the same year. References Central Intelligence Agency. (n.d.). The World Factbook. Central Intelligence Agency. Retrieved from: https://www.cia.gov/library/publications/the-world-factbook/. The World Bank. (2015). European Union. The World Bank. Retrieved from: http://data.worldbank.org/region/EUU. Appendix A: Summary Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent GDPpercapita 25 100.0% 0 0.0% 25 100.0% Appendix B: Descriptive statistics Descriptives Statistic Std. Error GDPpercapita Mean 34084.0000 3047.40152 95% Confidence Interval for Mean Lower Bound 27794.4724 Upper Bound 40373.5276 5% Trimmed Mean 32318.8889 Median 29200.0000 Variance 232166400.000 Std. Deviation 15237.00758 Minimum 16800.00 Maximum 91900.00 Range 75100.00 Interquartile Range 18000.00 Skewness 2.340 .464 Kurtosis 8.019 .902 Appendix C: Percentiles Percentiles Percentiles 5 10 25 50 Weighted Average(Definition 1) GDPpercapita 17070.0000 19440.0000 24600.0000 29200.0000 Tukeys Hinges GDPpercapita 25500.0000 29200.0000 Appendix C-continued Percentiles Percentiles 75 90 95 Weighted Average(Definition 1) GDPpercapita 42600.0000 46120.0000 78490.0000 Tukeys Hinges GDPpercapita 41400.0000 Appendix D: Mode Statistics GDPpercapita N Valid 25 Missing 0 Mode 16800.00a a. Multiple modes exist. The smallest value is shown Appendix D: X2 Statistics sqrGDPpercapita N Valid 25 Missing 0 Sum 34614970000.00 Read More