1 Develop a 1000-word response that answers each of the following prompts: Define statistics with citation and reference. Contrast quantitative data and qualitative data. Use two Peer Reviewed references. Evaluate tables and charts used to represent quantitative and qualitative data. Describe the levels of data measurement. Describe the role of statistics in business decision-making. Provide at least two business research questions, or problem situations, in which statistics was used or could be used. Use two peer reviewed references. Format your assignment consistent with APA guidelines. ASSIGNMENT 2 You are employed as a statistician for a company that makes household products, which are sold by part-time salespersons who work during their spare time. The company has four salespersons employed in a small town. Let us denote these salespersons by A, B, C, and D. The sales records (in dollars) for the past 6 weeks for these four salespersons are shown in the table below. Week A B C D 1 1774 2205 1330 1402 2 1808 1507 1295 1665 3 1890 2352 1502 1530 4 1932 1939 1104 1826 5 1855 2052 1189 1703 6 1726 1630 1441 1498 Your supervisor has asked you to prepare a brief report comparing the sales volumes and the consistency of sales of these four salespersons. Use the mean sales for each salesperson to compare the sales volumes. Choose an appropriate statistical measure to compare the consistency of sales. Make the calculations and write a 700-word report comparing the sales volumes and the consistency of sales of these four salespersons. Format your assignment consistent with APA guidelines. \fAssignment 1 and 2 by Benson Kariuki FILE ASSIGNMENT _1_ND_2.DOCX (28.2K) T IME SUBMIT T ED 01-SEP-2016 10:47AM WORD COUNT 1324 SUBMISSION ID 700186369 CHARACT ER COUNT 6614 Assignment 1 and 2 ORIGINALITY REPORT 7 3 0 5 % % % % SIMILARIT Y INDEX INT ERNET SOURCES PUBLICAT IONS ST UDENT PAPERS PRIMARY SOURCES 1 2 3 2 www.boundless.com % Int ernet Source 2 Submitted to Iqra Uninversity, Gulshan St udent Paper % Submitted to Emirates Aviation College, Aerospace & Academic Studies % 1 St udent Paper 4 1 akpublic.research.att.com % Int ernet Source EXCLUDE QUOT ES ON EXCLUDE BIBLIOGRAPHY ON EXCLUDE MAT CHES < 12 WORDS Assignment 1 Statistics According to Mendenhall 1985, Statistics is a branch in mathematics that involves application of quantitative procedures to collecting, analyzing, and presenting numerical data. Mendenhall also notes that statistics utilizes data of a sample drawn from a population describing it meaningfully, drawing sound conclusions and also making correct and sound decisions. Statisticians are individuals who are skilled in statistics and their job is to determine quantitative models that are applicable in given situations and also deciding what type of data that should be collected and analyzed. Applied statistics is a part of statistics that is concerned with the application of the general methodology to a given phenomenon. Difference between Quantitative and qualitative data From definition, Quantitative data is data that can be quantified or expressed as a number. For Example Weight, height, test score, number of hours of study, number of students in a class are all quantitative data. The measurement scales that represent this data are interval, ordinal or ratio scales and are important in classification of the data based on its level of measurement. Qualitative data on the other hand cannot be expressed numerically. It is Data that represent nominal scales which includes socio economic status, religious beliefs or gender. It is only quantitative data which is analyzable statistically, and thus its more rigorous in the assessments of the data. Representing Quantitative data Quantitative data can be represented in three common displays. Box-plot This is a graphical display of quantitative data in which a box represents the middle half of experimental unit. The line within the box represents at the middle of the distribution is the median and those lines that extend to the highest and lowest scores that are the outliers. Histogram: Here, vertical (or rarely horizontal) strands/bars are used to show the number of experimental units in each range of the values. The bars touch each other. An advantage of using box-plots and histograms is that their construction is relatively easy for a large data set. A disadvantage however is that individual observations are usually not specified. Stem and leaf plot It is a graphical representation for quantitative data whereby individual observations are displayed using numerical numbers. Usually all digits except for the final digits are in the stem column and the final digits are in the leaf column. Displaying Qualitative Data Pie Charts In pie charts, every category is shown by a portion of the pie graph. The area of each portion is proportional to the % of responses in a category. Bar Charts Bar charts are important in representing frequencies of the different observations that are in categories. We place the frequencies on the Y axis and observations on the X axis. . Measurement Levels Nominal Scale It depicts a categorical level of measurement. Values that are assigned to variables represent a descriptive category. E.g Gender and religious status Ordinal Scale In ordinal scale, there is the property of identity and magnitude. Each element on the scale has its own meaning. The relationship is also ordered with ranks. An example is level of education where we can state that primary level is below secondary level and tertiary level being the highest. Interval Scale In interval scale, absolute zero does not exist in the measurement. An example of an interval scale is temperature. This scale is made up of equal intervals. Observing a case where a temperature of between 20 and 30 degrees is equivalent to a temperature of between 80 to 90 degrees and thus the difference between 20 and 30 degrees is equivalent to that between 80 and 90 degrees. Note that we cannot stat that 0 degrees represents no temperature. Ratio Scale Ratio scale possesses the qualities of other measurement scales. Additionally, absolute zero exists. Using a ratio scale allows us to compare situations such as being two times as much, or half as much. Example includes exam score whereby zero means no score. Role of Statistics in Decision Making Planning Statistics enables a manager to plan for produce based on the taste of his/her costumers. Quality of goods can also be investigated more conveniently using statistical quality controls principles. Therefore, all the decisions of the manager are based on statistical knowledge. He can make sound decisions about the location of enterprise, financial resources and marketing of his products, Backing Decisions Statistics is useful in supporting assumptions that are felt to be true. Often times, Managers come up with assertions which they must use to convince their bosses or persuade their clients on. Using Statistical procedures, they can provide a clear road map on how the assertions will impact the direction to which the business is headed. Making Relationships Existing relationships can be pointed out in the business by use of statistics. This entails a Careful review of data and thus reveals important associations if they exist between two or more variables. The variables may include, does advertising cost affect the level of sales? Or does training increase employee productivity? Scrutinizing the data in details can provide more information about the links to investigate thus controlling customer satisfaction, recurring purchases and thus improvement in sales. Quality Assurance Any successful business needs to have a quality assurance department. In quality assurance, statistical principles of quality control are crucial. The manager is then able to understand how the products of the business are rated by the customers and what needs to be done to improve customer perceptions. Also, production cost and labour contribution are evaluated and thus a decision on how to cut cost or vary the labour force is made. Assignment 2 Sales Person A: Mean will be found by averaging sales for the six weeks. 1774 +1808+1890+1932+1855+1726 6 = 1830.833 B: The average is; 2205+ 1507+2352+1939+2052+1630 6 = 1947.500 C: The average is; 1330+1295+ 1502+1104 +1189 +1441 6 = 1310.167 D: Average is; 1402+1665+1530+1826+ 1703+1498 6 = 1604.000 From the results, Supplier B delivers the highest batch of goods for the 6 weeks on average with a mean volume of 1947.5. Supplier A closely follows in mean average with an average of 1830.833. Supplier C had the least mean supply volume within the 6 weeks of 1310.167 while supplier D delivered slightly much than C at 1604. For consistency, we will investigate the variance and standard deviation of each supplier within the 6 weeks. For Supplier A, = 5812.167 2 (X X )2 N1 = 76.238 Supplier B, The formulas as used above apply and thus we get; 2 (X X )2 N1 2 (X X )2 N1 89294.25 for the variance. 89294.25 = 298.82 Supplier C, Repeating the procedure above; Var=18621.139 Standard deviation = 18621.139 = 136.459 Supplier D, As above, Var =20053.667 Standard deviation = 20053.667 = 141.611 From the results, supplier A was most consistent since he had the least standard deviation of 76.238 while supplier B was the most inconsistent with a standard deviation of 298.82. Supplier C and D had a standard deviation of 136.459 and 141.611 respectively and thus supplier C was more consistent that D because the standard deviation was lower for C. References 1. https://www.boundless.com/statistics/textbooks/boundless-statistics-textbook/frequencydistributions-4/frequency-distributions-for-qualitative-data-21/graphs-of-qualitative-data106-97/ 2. Ott, L., & Mendenhall, W. (1985). Understanding statistics. Duxbury Resource Center. .............................................................................. . . . . . . . . . . . . END . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \fAssignment 1 and 2 by Benson Kariuki FILE ASSIGNMENT _1_ND_2.DOCX (28.2K) T IME SUBMIT T ED 01-SEP-2016 10:47AM WORD COUNT 1324 SUBMISSION ID 700186369 CHARACT ER COUNT 6614 Assignment 1 and 2 ORIGINALITY REPORT 7 3 0 5 % % % % SIMILARIT Y INDEX INT ERNET SOURCES PUBLICAT IONS ST UDENT PAPERS PRIMARY SOURCES 1 2 3 2 www.boundless.com % Int ernet Source 2 Submitted to Iqra Uninversity, Gulshan St udent Paper % Submitted to Emirates Aviation College, Aerospace & Academic Studies % 1 St udent Paper 4 1 akpublic.research.att.com % Int ernet Source EXCLUDE QUOT ES ON EXCLUDE BIBLIOGRAPHY ON EXCLUDE MAT CHES < 12 WORDS Assignment 1 Statistics According to Mendenhall 1985, Statistics is a branch in mathematics that involves application of quantitative procedures to collecting, analyzing, and presenting numerical data. Mendenhall also notes that statistics utilizes data of a sample drawn from a population describing it meaningfully, drawing sound conclusions and also making correct and sound decisions. Statisticians are individuals who are skilled in statistics and their job is to determine quantitative models that are applicable in given situations and also deciding what type of data that should be collected and analyzed. Applied statistics is a part of statistics that is concerned with the application of the general methodology to a given phenomenon. Difference between Quantitative and qualitative data From definition, Quantitative data is data that can be quantified or expressed as a number. For Example Weight, height, test score, number of hours of study, number of students in a class are all quantitative data. The measurement scales that represent this data are interval, ordinal or ratio scales and are important in classification of the data based on its level of measurement. Qualitative data on the other hand cannot be expressed numerically. It is Data that represent nominal scales which includes socio economic status, religious beliefs or gender. It is only quantitative data which is analyzable statistically, and thus its more rigorous in the assessments of the data. Representing Quantitative data Quantitative data can be represented in three common displays. Box-plot This is a graphical display of quantitative data in which a box represents the middle half of experimental unit. The line within the box represents at the middle of the distribution is the median and those lines that extend to the highest and lowest scores that are the outliers. Histogram: Here, vertical (or rarely horizontal) strands/bars are used to show the number of experimental units in each range of the values. The bars touch each other. An advantage of using box-plots and histograms is that their construction is relatively easy for a large data set. A disadvantage however is that individual observations are usually not specified. Stem and leaf plot It is a graphical representation for quantitative data whereby individual observations are displayed using numerical numbers. Usually all digits except for the final digits are in the stem column and the final digits are in the leaf column. Displaying Qualitative Data Pie Charts In pie charts, every category is shown by a portion of the pie graph. The area of each portion is proportional to the % of responses in a category. Bar Charts Bar charts are important in representing frequencies of the different observations that are in categories. We place the frequencies on the Y axis and observations on the X axis. . Measurement Levels Nominal Scale It depicts a categorical level of measurement. Values that are assigned to variables represent a descriptive category. E.g Gender and religious status Ordinal Scale In ordinal scale, there is the property of identity and magnitude. Each element on the scale has its own meaning. The relationship is also ordered with ranks. An example is level of education where we can state that primary level is below secondary level and tertiary level being the highest. Interval Scale In interval scale, absolute zero does not exist in the measurement. An example of an interval scale is temperature. This scale is made up of equal intervals. Observing a case where a temperature of between 20 and 30 degrees is equivalent to a temperature of between 80 to 90 degrees and thus the difference between 20 and 30 degrees is equivalent to that between 80 and 90 degrees. Note that we cannot stat that 0 degrees represents no temperature. Ratio Scale Ratio scale possesses the qualities of other measurement scales. Additionally, absolute zero exists. Using a ratio scale allows us to compare situations such as being two times as much, or half as much. Example includes exam score whereby zero means no score. Role of Statistics in Decision Making Planning Statistics enables a manager to plan for produce based on the taste of his/her costumers. Quality of goods can also be investigated more conveniently using statistical quality controls principles. Therefore, all the decisions of the manager are based on statistical knowledge. He can make sound decisions about the location of enterprise, financial resources and marketing of his products, Backing Decisions Statistics is useful in supporting assumptions that are felt to be true. Often times, Managers come up with assertions which they must use to convince their bosses or persuade their clients on. Using Statistical procedures, they can provide a clear road map on how the assertions will impact the direction to which the business is headed. Making Relationships Existing relationships can be pointed out in the business by use of statistics. This entails a Careful review of data and thus reveals important associations if they exist between two or more variables. The variables may include, does advertising cost affect the level of sales? Or does training increase employee productivity? Scrutinizing the data in details can provide more information about the links to investigate thus controlling customer satisfaction, recurring purchases and thus improvement in sales. Quality Assurance Any successful business needs to have a quality assurance department. In quality assurance, statistical principles of quality control are crucial. The manager is then able to understand how the products of the business are rated by the customers and what needs to be done to improve customer perceptions. Also, production cost and labour contribution are evaluated and thus a decision on how to cut cost or vary the labour force is made. Assignment 2 Sales Person A: Mean will be found by averaging sales for the six weeks. 1774 +1808+1890+1932+1855+1726 6 = 1830.833 B: The average is; 2205+ 1507+2352+1939+2052+1630 6 = 1947.500 C: The average is; 1330+1295+ 1502+1104 +1189 +1441 6 = 1310.167 D: Average is; 1402+1665+1530+1826+ 1703+1498 6 = 1604.000 From the results, Supplier B delivers the highest batch of goods for the 6 weeks on average with a mean volume of 1947.5. Supplier A closely follows in mean average with an average of 1830.833. Supplier C had the least mean supply volume within the 6 weeks of 1310.167 while supplier D delivered slightly much than C at 1604. For consistency, we will investigate the variance and standard deviation of each supplier within the 6 weeks. For Supplier A, = 5812.167 2 (X X )2 N1 = 76.238 Supplier B, The formulas as used above apply and thus we get; 2 (X X )2 N1 2 (X X )2 N1 89294.25 for the variance. 89294.25 = 298.82 Supplier C, Repeating the procedure above; Var=18621.139 Standard deviation = 18621.139 = 136.459 Supplier D, As above, Var =20053.667 Standard deviation = 20053.667 = 141.611 From the results, supplier A was most consistent since he had the least standard deviation of 76.238 while supplier B was the most inconsistent with a standard deviation of 298.82. Supplier C and D had a standard deviation of 136.459 and 141.611 respectively and thus supplier C was more consistent that D because the standard deviation was lower for C. References 1. https://www.boundless.com/statistics/textbooks/boundless-statistics-textbook/frequencydistributions-4/frequency-distributions-for-qualitative-data-21/graphs-of-qualitative-data106-97/ 2. Ott, L., & Mendenhall, W. (1985). Understanding statistics. Duxbury Resource Center. .............................................................................. . . . . . . . . . . . . END