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BUSINESS STATISTICS AND PROBABILITY Chapter 1 By Arbaminich University
- 1. CHAPTER 1 INTRODUCTION TO BUSINESS STATISTICS In a business environment managers can make sound decisions when they use all relevant information in an effective and meaningful manner. The principal purpose of statistics is to provide decision-makers with a set of techniques for collecting, analyzing, and draw meaningful inferences that lead to improved decisions. Now a day, statistical tools are widely used to aid decision-makers in all functional areas of management. The purpose of this chapter is to provide you the basic ideas and concepts of statistics at a general level.
- 2. What is Statistics? Different authors define statistics differently based on their area of concern of this; Statistics is defined as the science which deals with the method of collecting, classifying, presenting, comparing, and interpreting numerical data “Seligman”. A.L. Bowley has defined statistics as: statistics is the science of counting. Statistics may rightly be called the science of averages statistics is the science of measurement of social organism regarded as a whole in all its manifestations.
- 3. CONT… Croxton and cowden have defined statistics as science of collecting, presentation, analysis, and interpretation of numerical data. Statistics is defined as the science of estimates and probabilities “Boddington”. Generally for our purpose statistics is defined as methods specially adapted to the collection, classification, analysis, and interpretation of data for making effective decisions in all functional areas of management.
- 4. Types of Statistics Statistics can be classified in to two major categories 1. Descriptive Statistics It includes statistical methods involving the collection, presentation, and characterization of a set of data in order to describe the various features of the set of data. Method of descriptive statistics includes: graphic methods (like bar graph, line graph, pie chart, o-give chart…) and numerical measures (such as measure of central tendency/mean, median, mode etc.) and measures of dispersion(variance, co-variance and standard deviation).
- 5. CONT… 2. Inferential statistics Is the process of reaching generalizations about the whole (called the population) by examining a portion (called the sample). It is used to predict the future possibilities. In order for this to be valid, the sample must be representative of the population and the probability of error also must be specified. It includes point estimation, interval estimation and hypothesis testing. Caution: Inferential Statistics assumes that the sampling methodology is random (i.e. based on probability sampling).
- 6. Key terms in Statistics Population - is the collection of all possible observations of a specified characteristic of interest. Sample – is the portion or part of the population of interest. Element – entity on which data are collected. Census or complete enumeration: - a study that includes every member of the target population, but it is too costly & time consuming. Parameter – is the population characteristics of interest. Statistic – is the characteristics of sample. Variable- is a characteristic that assumes different values for different elements.
- 7. Types of Data A. Based on quantifiable Qualitative Data - are non-numeric in nature and can't be measured. Examples are gender/sex, color, religion, nationality, marital status and place of birth. Quantitative Data - are numerical in nature and can be measured. Examples are height, weight, amount of rain fall, age, balance in your savings bank account and number of computers in a given class. Quantitative data can be classified into discrete and continuous type. Discrete type - values are obtained by counting, and the possible values are (0, 1, 2, 3, 4, 5, 6, 7, 8 …) which cannot be in fraction. Continuous type – determined by measurement and its value include decimal values. Such as, distance between two towns, weight of a person, height …etc
- 8. CONT… B. Based on data source Primary data: - are data which do not already exist in any form, and thus have to be collected for the first time from the primary source(s). By their very nature, these data require fresh and first-time collection covering the whole population or a sample drawn from it. The benefits of primary data are that they fit the needs exactly, are up to date, and reliable/genuine/. And its disadvantage is it is costly and time taking. Secondary data: - are those which have already been collected by some one else and which have already passed through the statistical process. They already exist in some form: published or unpublished - in an identifiable secondary source. Secondary data have the advantages of being much cheaper and faster to collect. And its disadvantage is it is not reliable.
- 9. CONT… C. Based on the time data collected Cross sectional data: - this is data collected at the same time or one particular point in time on different elements. For example, sales made at the same point in time but at different market places. Time series (longitudinal) data: - this is data collected at several points in time from the same study objects or units. It helps to see increasing or decreasing trends over time. For example, sales data for different periods.
- 10. Types of Data Measurement Nominal data The weakest data measurement. Under nominal data numbers are used only for coding and labeling /categorizing nominal data/items. For example; nominal data includes gender (while we are collecting data we may represent, 0= male and 1 = female). Ordinal data numbers are used to order and rank data. Ordinal data can also be verbalized on a continuum like excellent, very good, good, fair and poor. For example; Customer Preference for your brand could be rated as excellent, good and poor.
- 11. CONT… Interval data Interval data are superior to ordinal data because with them decision makers can measure the distance between two observations (i.e., the difference between value of interval has meaning). Temperature is a typical example of interval data, it is expressed as cool (5 - 15), moderate (16 - 26, and high (27 – 37). Ratio data It is the highest level of measurement and allows you to perform all basic arithmetic operations, including division, multiplication, logarithm, and power.
- 12. Application Areas of Statistics 1. Marketing Before the new product is launched, the market research team of an organization, through a pilot survey, use various techniques to analyze data on population; purchasing power, competitors, habits of consumers, pricing and advertising strategies. 2. Production Statistical methods are used to carry out R&D programs for improvement in the quality of the existing products, identifying and rejecting defective or substandard goods and setting quality control standards for new ones and also, decision about manufacturing/buying raw materials for production.
- 13. CONT… 3. Finance A statistical technique through correlation analysis of profit dividend helps to predict and decide probable dividend for future years. In addition, the level of expense for advertising and sales volume also determined by using statistics. 4. Personnel In the process of man power planning, a personnel department makes statistical studies of wage rate, incentive plans, cost of living, and labor turnover rate, employment trends, accident rates, performance appraisal, training and development.
- 14. Limitations of Statics Statistics has a number of limitations, pertinent among them are as follows: Statistical results are true only on average. i.e. reveal the average behavior, the normal or the general trend Statistics deals with aggregate. an individual observation cannot be considered as statistics. The difference between the true value and the estimated value are not the same /bias. Misuse of statistics statistical results may be misused knowingly or unknowingly, in different ways.
- 15. Scopes of Statistical Investigation Depending on their coverage, statistical investigations are usually carried out either in the form of census or sample survey. 1. Census A census is the one in which all the units connected with the problem are taken into account. Complete enumeration is the basic characteristic of census. In census approach data is gathered from each and every member in the population (universe).
- 16. CONT… Information is available for each separate part of the universe. The results to be obtained are likely to be more representative, accurate and reliable. It serves as a basis for various surveys, because it is free from sampling error. Easier to check and reduce coverage error. Advantage of census It requires very large effort, money and time. In case where the population is infinite, census approach can’t be applied. Limitation of census
- 17. 2. Sample survey Sample survey refers to the collection of information about a variable of interest from only some part (or subset) of the population called sample. Sample elements are selected from a population through different alternative sampling techniques. In sample survey only some selected representative units are studied.
- 18. CONT… It reduces cost It saves labor. It enables advanced tabulation of selected topics. Sometimes conducting a sample survey is the only option for study. Sample survey may be used to test census procedures and updating census results. Advantages of sample survey Requires trained personnel for data collection purpose. Does not give reliable results without careful planning and design. It has the task of sample size determination and sample selection. Sample survey involves sampling error. Limitation of sample survey