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## qnt 351 Summarizing and Presenting

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# qnt 351 Summarizing and Presenting

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Date Created: 11/14/15
Summarizing and Presenting Data Summarizing and Presenting Data  Team C  Erin E. DeVera, Robin Evans, Cheryl Houston,  Craig Isaac, Burnadette Johnson, Tiffany Pena, Darren Smith  QNT/351  June 25, 2012  Alemayehu Lirenso, PhD  Summarizing and Presenting Data  Summarizing data effectively to communicate concepts with clarity to ensure an understanding  by an audience is important when presenting. The central location comprised of mean, median,  and mode, followed by the measure of dispersion; standard deviation, variance, skewness, and  coefficient of variation are used to evaluate wages, education level, and work experience.  Bivariate charts in the form of bar, histogram, line or pie graphs are an effective method of  displaying key findings necessary for data analyst and interpretations.  Central Location  Measure of central location is a measure of location within a distribution and summarizes the one score that best describes the centrality of the data. The measure of tendency that best represents  the data set in this example is the median for wages as it represents a good indicator of the  typical salary within the data set.  |  |  |Mean |Median |Mode |  |Wages |\$3,083,346 |\$30,833.46 |\$43,036 |\$20,852 |  |Education |1273 |12.73 |18 |12 |  |Experience |2038 |20.38 |27.5 |(6, 10) |  Measure of Dispersion  The standard deviation for the wage variable is 16,947.097270249 (16947.10 rounded). This data set has a variance of 287204105.88727 (287204105.89 rounded). This sample has a coefficient  of variation of 0.54963332919 (0.55 rounded). The box and whiskers plot shows a skewness of  1.340025731 (1.34 rounded) that indicates the tail is to the right, and the wages between \$55,777 and \$83,601 are extreme outliers for this data set. Outliers in this set could mean that more  workers are paid within a reasonable amount and only a select few are paid more.  [pic]  The standard deviation for the education variable is 2.791961766402 (2.79 rounded). This data  set has a variance of 7.7950505050505 (7.80 rounded). This sample has a coefficient of variation of 0.21932142705 (0.22 rounded). The box and whiskers plot shows a skewness of ­0.315 (­0.32  rounded) that indicates the tail is to the left and the years of education between four and eight are extreme outliers and 16 and 18 are just outliers closer to the norm for this data set. Outliers in  this set could mean that the average years of education that each worker has is just about the  same amount. This set has outliers both positively and negatively because the skewness is  negative this means that the tail on the left is much more extended than the one on the right.  [pic]  The standard deviation for the years of experience variable is 13.549594648974 (13.55 rounded). This data set has a variance of 183.59151515152 (183.59 rounded). This sample has a coefficient of variation of 0.66484762752 (0.66 rounded). The box and whiskers plot shows a skewness of  0.482 (0.48 rounded) that indicates the tail is to the right and the years of experience at 54 and  above are extreme positive outliers for this data set. Of the 100 sample wage earners the only  outlier is 54. Outliers in this set could mean that more workers are not staying in one particular  job longer than 47 years and averaging between six and 20 years on­ the­job experience.  [pic]  Frequency Tables  Frequency tables are used to present statistical data by assigning values of a characteristic by the  number of times that value exists in the data tables (Statistics Canada, 2012). The annual wages  graph indicates 19 incidents of wages between \$30,000 and \$34,999. The bar graph clearly  indicates the most frequent value.  [pic]  The education frequency graph provides a clear summation that 12 years within the education  system is the most common among employees.  [pic]  The employee experience graph is a good indication that employees have many years of  experience within the company. The bar graph clearly indicates 10 employees out to the 100  have between 40 and 49 years of experience.  [pic]  Bivariate Relationship Review  Below is the graphical relationship of the wage earner’s wages to their years of experience. The  quantitative data for these two variables were plotted onto a scatter gram. From this bivariate  relationship, the conclusion can be made that the years of experience does not necessarily have  any bearing on the amount of wages earned. There are plots where the highest years of  experience are earning only around \$20,000 and others that worked between five to 10 years and  are making the highest wages. There is no clear trend between the relationships of these two  variables.  [pic]  A Comparison of Wages and Years of Education  The data set used contained a sample of 100 people. Each person listed data for wages,  education, experience, and other factors that could affect income. In this section wages and  education are compared.  To compare wages and education a scatter plot, a bar graph, and a line chart were used. The  scatter plot shown below suggests education is positively correlated with income. The  expectation suggests individuals with additional years of education have a higher annual average  wage. However, the correlation is not conclusive as there are examples of individuals with fewer  years of education earning higher incomes.  An interesting cluster on the scatter plot occurs at 12 years of education as many people have this level of education, possibly because many people graduate high school after grade 12 and do not  continue to pursue a post­secondary education. There is also a wide range of income levels  among these high school graduates. The average wages for this group range from \$10,000 to  \$50,000.  [pic]  To get a clearer picture of the relationship between wages and education, the average wage for  each year of education was calculated using the excel function “AVERAGEIF.” The bar graph  indicates the average wage at each level of income. This graph also suggests that higher levels of education are paired with elevated income levels with some exceptions.  |Years of Education |1 |2 |  | \$ 9,879 |4 |0 |  | \$ 10,997 |5 |0 |  | \$ 11,186 |6 |1 |  | \$ 11,451 |7 |3 |  | \$ 11,702 |8 |3 |  | \$ 11,780 |8 |3 |  | \$ 12,285 |8 |4 |  | \$ 13,162 |8 |4 |  | \$ 13,312 |9 |4 |  | \$ 13,318 |9 |4 |  | \$ 13,481 |10 |5 |  | \$ 13,787 |10 |5 |  | \$ 14,476 |10 |5 |  | \$ 15,013 |11 |6 |  | \$ 15,160 |11 |6 |  | \$ 15,193 |11 |6 |  | \$ 15,234 |11 |6 |  | \$ 15,957 |11 |6 |  | \$ 16,667 |12 |7 |  | \$ 16,789 |12 |7 |  | \$ 16,796 |12 |7 |  | \$ 16,817 |12 |7 |  | \$ 17,626 |12 |8 |  | \$ 17,690 |12 |8 |  | \$ 17,694 |12 |9 |  | \$ 18,121 |12 |9 |  | \$ 18,752 |12 |9 |  | \$ 19,227 |12 |10 |  | \$ 19,284 |12 |10 |  | \$ 19,306 |12 |10 |  | \$ 19,388 |12 |10 |  | \$ 19,452 |12 |10 |  | \$ 19,981 |12 |11 |  | \$ 20,793 |12 |12 |  | \$ 20,852 |12 |12 |  | \$ 20,852 |12 |12 |  | \$ 21,716 |12 |12 |  | \$ 21,994 |12 |13 |  | \$ 22,133 |12 |14 |  | \$ 22,485 |12 |14 |  | \$ 23,027 |12 |14 |  | \$ 24,509 |12 |14 |  | \$ 25,166 |12 |15 |  | \$ 25,670 |12 |15 |  | \$ 26,614 |12 |15 |  | \$ 26,795 |12 |15 |  | \$ 26,820 |12 |17 |  | \$ 28,168 |12 |18 |  | \$ 28,219 |12 |18 |  | \$ 28,440 |12 |18 |  | \$ 29,191 |12 |19 |  | \$ 29,390 |12 |19 |  | \$ 29,407 |12 |19 |  | \$ 29,736 |12 |20 |  | \$ 29,809 |12 |20 |  | \$ 29,977 |12 |21 |  | \$ 30,006 |12 |21 |  | \$ 30,133 |12 |22 |  | \$ 30,308 |12 |22 |  | \$ 31,304 |12 |22 |  | \$ 31,691 |12 |24 |  | \$ 31,702 |13 |24 |  | \$ 31,799 |13 |24 |  | \$ 32,094 |13 |25 |  | \$ 32,138 |13 |25 |  | \$ 32,235 |13 |26 |  | \$ 32,786 |13 |26 |  | \$ 33,351 |14 |26 |  | \$ 33,389 |14 |26 |  | \$ 33,411 |14 |27 |  | \$ 33,461 |14 |27 |  | \$ 33,498 |14 |28 |  | \$ 33,959 |14 |28 |  | \$ 34,484 |14 |29 |  | \$ 34,746 |14 |29 |  | \$ 35,185 |14 |29 |  | \$ 36,178 |15 |31 |  | \$ 37,664 |15 |33 |  | \$ 37,771 |15 |33 |  | \$ 39,888 |16 |33 |  | \$ 41,780 |16 |34 |  | \$ 44,543 |16 |34 |  | \$ 45,976 |16 |37 |  | \$ 46,646 |16 |38 |  | \$ 49,898 |16 |38 |  | \$ 49,974 |16 |38 |  | \$ 50,171 |16 |38 |  | \$ 50,187 |16 |39 |  | \$ 50,235 |16 |39 |  | \$ 52,762 |16 |40 |  | \$ 55,777 |16 |42 |  | \$ 57,623 |17 |43 |  | \$ 60,152 |17 |44 |  | \$ 60,626 |17 |44 |  | \$ 66,738 |18 |45 |  | \$ 68,573 |18 |45 |  | \$ 75,165 |18 |45 |  | \$ 83,443 |18 |45 |  | \$ 83,569 |18 |47 |  | \$ 83,601 |18 |54 |  |  |  |  |  | \$ 3,083,346 |1273 |2038 |  Wages Bin |Frequency | |Education Bin |Frequency | |Experience Bin |Frequency | |9500­9999 |1 | |4 |1 | |0 |2 | |10000­10999 |1 | |5 |1 | |1 |1 | |11000­11999 |4 | |6 |1 | |2 |0 | |12000­12999 |1 | |7 |1 | |3  |3 | |13000­13999 |5 | |8 |4 | |4 |4 | |14000­14999 |1 | |9 |2 | |5 |3 | |15000­15999 |5 | |10 |3 | |6 |5 | | 16000­16999 |4 | |11 |5 | |7 |4 | |17000­17999 |3 | |12 |43 | |8 |2 | |18000­18999 |2 | |13 |6 | |9 |3 | | 19000­19999 |6 | |14 |9 | |10 |5 | |20000­24999 |9 | |15 |3 | |11 |1 | |25000­29999 |14 | |16 |12 | |12 |4 | |30000­34999 |19 | |17 |3 | |13 |1 | |35000­39999 |5 | |18 |6 | |14 |4 | |40000­44999 |2 | | | | |15 |4 | | 45000­49999 |4 | | | | |16 |0 | |50000­54999 |4 | | | | |17 |1 | |55000­59999 |2 | | | | |18 |3 | |60000­ 69999 |4 | | | | |19 |3 | |70000­79999 |1 | | | | |20 |2 | |80000­89999 |3 | | | | |21 |2 | | | | | | | |22 |3 | | | | | |  | |23 |0 | | | | | | | |24 |3 | | | | | | | |25 |2 | | | | | | | |26 |4 | | | | | | | |27 |2 | | | | | | | |28 |2 | | | | | | | |29 |3 | | | | | |  | |30­34 |6 | | | | | | | |35­39 |7 | | | | | | | |40­49 |10 | | | | | | | |50­59 |1 | |

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