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- 1. Introduction to Stats By Miss Kehkashan Nizam
- 2. Contents • Statistics • Applications of Statistics in Business and Economics • Descriptive Statistics • Inferential Statistics • Data • Data Sources
- 3. Statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied
- 4. Application of Statistics For the effective functioning of the State, Statistics is indispensable. Different department and authorities require various facts and figures on different matters. They use this data to frame policies and guidelines in order to perform smoothly. Traditionally, people used statistics to collect data pertaining to manpower, crimes, wealth, income, etc. for the formation of suitable military and fiscal policies. Over the years, with the change in the nature of functions of the State from maintaining law and order to promoting human welfare, the scope of the application of statistics has changed too. Today, the State authorities collect statistics through their agencies on multiple aspects like population, agriculture, defense, national income, oceanography, natural resources, space research, etc. Further, nearly all ministries at the Central as well as State level, rely heavily on statistics for their smooth functioning. Also, the availability of statistical information enables the government to frame policies and guidelines to improve the overall working of the system.
- 5. Application of Statistics Economics is about allocating limited resources among unlimited ends in the most optimal manner. Statistics offers information to answer some basic questions in economics What to produce?, How to produce?, For whom to produce? Statistical information helps to understand the economic problems and formulation of economic policies. Traditionally, the application of statistics was limited since the economic theories were based on deductive logic. Also, most statistical techniques were not developed enough for application in all disciplines. However, today, with computers and information technology, statistical data and advanced techniques of statistical analysis are a boon to many. In economics, many scholars have now shifted their stand from deductive logic to inductive logic in order to explain any economic proposition. This inductive logic requires the observation of economic behavior of a large number of units. Hence, it needs strong statistical support in the form of data and techniques.
- 6. Application of Statistics According to Chao, “Statistics is a method of decision-making in the face of uncertainty on the basis of numerical data and calculated risks.” Hence, statistics provides information to businesses which help them in making critical decisions. • Accounting--Public accounting firms use statistical sampling procedures when conducting audits for their clients. • Finance--Financial advisors use a variety of statistical information, including price-earnings ratios and dividend yields, to guide their investment recommendations. • Marketing--Electronic point-of-sale scanners at retail checkout counters are being used to collect data for a variety of marketing research applications..
- 7. Application of Statistics • Production-- A variety of statistical quality control charts are used to monitor the output of a production process. • Economics--Economists use statistical information in making forecasts about the future of the economy or some aspect of it. • Industry--Statistics helps in the field of Quality Control
- 8. Statistical methods used in data analysis Two main statistical methods are used in data analysis: • Descriptive statistics • Inferential Statistics
- 9. Descriptive Statistics Descriptive statistics are graphical representations of data in tabular, graphical, and numerical methods in order to summarize data. A graphical representation of data is a useful method of analysis. Examples of this visual representation are histograms, bar graphs and pie graphs, to name a few. Using these methods, the data is described by compiling it into a graph, table or other visual representation. This provides a quick method to make comparisons between different data sets and to spot the smallest and largest values and trends or changes over a period of time.
- 10. Descriptive Statistics Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): • Central tendency (or location) seeks to characterize the distribution's central or typical value, Use the mean or the median to locate the center of the dataset. This measure tells you where most values fall. • Dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. You can use the range or standard deviation to measure the dispersion. A low dispersion indicates that the values cluster more tightly around the center. Higher dispersion signifies that data points fall further away from the center. We can also graph the frequency distribution.
- 11. EXAMPLE The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed below. Find out mean, frequency and percentages. Make the histrogram. 91 78 93 57 75 52 99 80 97 62 71 69 72 89 66 75 79 75 72 76 104 74 62 68 97 105 77 65 80 109 85 97 88 68 83 68 71 69 67 74 62 82 98 101 79 105 79 69 62 73
- 12. EXAMPLE Numerical Descriptive Statistics • The most common numerical descriptive statistic is the average (or mean). • Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).
- 13. Inferential Statistics Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population). Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. Because the goal of inferential statistics is to draw conclusions from a sample and generalize them to a population, we need to have confidence that our sample accurately reflects the population. This requirement affects our process. At a broad level, we must do the following: • Define the population we are studying. • Draw a representative sample from that population. • Use analyses that incorporate the sampling error.
- 14. Inferential Statistics’ s Methodologies The most common methodologies in inferential statistics are • hypothesis tests • confidence intervals • regression analysis
- 15. Inferential Statistics’ s Methodologies
- 16. Data and Data Sets Data are characteristics or information, usually numerical, that are collected through observation. In a more technical sense, data is a set of values of qualitative or quantitative variables about one or more persons or objects, while a datum (singular of data) is a single value of a single variable. The data collected in a particular study are referred to as the data set
- 17. Definitions • The elements are the entities on which data are collected. • A variable is a characteristic of interest for the elements. • The set of measurements collected for a particular element is called an observation. • The total number of data values in a data set is the number of elements multiplied by the number of variables.
- 18. Definitions
- 19. Scales of Measurement Scales of measurement include: • Nominal • Ordinal • Interval • Ratio • The scale determines the amount of information contained in the data. • The scale indicates the data summarization and statistical analyses that are most appropriate.
- 20. Scales of Measurement Nominal Data are labels or names used to identify an attribute of the element. A nonnumeric label or a numeric code may be used. Example: Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on. Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3= denotes Education, and so on).
- 21. Scales of Measurement Ordinal • The data have the properties of nominal data and the order or rank of the data is meaningful. A nonnumeric label or a numeric code may be used. Example: Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).
- 22. Scales of Measurement Interval The data have the properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure. Interval data are always numeric. Example: Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.
- 23. Scales of Measurement Ratio The data have all the properties of interval data and the ratio of two values is meaningful. Variables such as distance, height, weight, and time use the ratio scale. This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. Example: Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.
- 24. Qualitative and Quantitative Data Data can be further classified as being qualitative or quantitative. The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative. In general, there are more alternatives for statistical analysis when the data are quantitative
- 25. Qualitative Data Qualitative data are labels or names used to identify an attribute of each element. Qualitative data use either the nominal or ordinal scale of measurement. Qualitative data can be either numeric or nonnumeric. The statistical analysis for qualitative data are rather limited.
- 26. Quantitative Data Quantitative data indicate either how many or how much. Quantitative data that measure how many are discrete. Quantitative data that measure how much are continuous because there is no separation between the possible values for the data.. Quantitative data are always numeric. Ordinary arithmetic operations are meaningful only with quantitative data.
- 27. Cross-Sectional and Time Series Data Cross-sectional data are collected at the same or approximately the same point in time. Example: data detailing the number of building permits issued in June 2000 in each of the counties of Texas Time series data are collected over several time periods. Example: data detailing the number of building permits issued in Travis County, Texas in each of the last 36 months
- 28. Cross-Sectional and Time Series Data Primary data: Data collected by the investigator himself/ herself for a specific purpose. Examples: Data collected by a student for his/her thesis or research project. ... Secondary data: Data collected by someone else for some other purpose , from existing Sources • Data needed for a particular application might already exist within a firm. Detailed information is often kept on customers, suppliers, and employees for example. • Substantial amounts of business and economic data are available from organizations that specialize in collecting and maintaining data. • Government agencies are another important source of data. • Data are also available from a variety of industry associations and special-interest organizations. • The Internet has become an important source of data
- 29. Types of Data Primary data: Data collected by the investigator himself/ herself for a specific purpose. Examples: Data collected by a student for his/her thesis or research project. ... Secondary data: Data collected by someone else for some other purpose , from existing Sources • Data needed for a particular application might already exist within a firm. Detailed information is often kept on customers, suppliers, and employees for example. • Substantial amounts of business and economic data are available from organizations that specialize in collecting and maintaining data. • Government agencies are another important source of data. • Data are also available from a variety of industry associations and special-interest organizations. • The Internet has become an important source of data
- 30. Data Acquisition Considerations Time Requirement--Searching for information can be time consuming. Information might no longer be useful by the time it is available. Cost of Acquisition--Organizations often charge for information even when it is not their primary business activity. Data Errors--Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information.
- 31. Data Acquisition Considerations Time Requirement--Searching for information can be time consuming. Information might no longer be useful by the time it is available. Cost of Acquisition--Organizations often charge for information even when it is not their primary business activity. Data Errors--Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information.