Chapter 1 - Introduction PDF

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INTRODUCTION TO STATISTICS This first chapter intends to explain the meaning of Statistics, the contents of descriptive and inferential Statistics, followed by the most important concepts used by Statistics.

1.1 Introduction For a better understanding of Statistics meaning bear in mind that this word is used to express several different situations, facts, reports. Usually the word statistics is used to nominate a set of numbers. In its earlier and still most common usage, statistics means a collection of numerical facts or data. The word “statistics” commonly brings to mind masses of numbers, graphs and tables. The scientific meaning is assigned to a science developing its own methods concerning data collection, summarizing, organizing and analysing followed by conclusions used as a decision background by the managers. Also among the scientific meaning of “Statistics”, which is the most important thing in this book is the measure, the indicators computed for a data set.

Statistics for Business Administration

The purpose of Statistics as a science is to summarize the essential features and relationships of the masses of numerical data in order to determine patterns of behaviour, particular outcomes or future tendencies. Statistics is a way of getting information from data, studying large collectivities, and not being interested in individuals. Statistics aims to establish stable characteristics expressed by a statistical law (conclusion); this can be applied only for the whole collectivity, not for individuals. One of the main objectives of Statistics is to provide a set of procedures that enables us to make inferences, prediction and to take decisions about the characteristics of a population by using a sample. As a discipline, Statistics has advanced rapidly during the twentieth century to become recognized as a branch of Mathematics. The main distinction between our definition and the common meaning of the word “Statistics” is its form, plural versus singular. Statistics (singular) is a subject of study while Statistics (plural) are numerical facts. Finally, we can conclude that Statistics is the science that deals with the collection, classification, analysis and interpretation of numerical facts or data. It means that by the use of mathematical theories of probability it imposes order and regularity on aggregate of disparate elements of the same population. Our course covers statistical methods for decision making in Business Administration and Economics.

1.2 Descriptive and Inferential Statistics Statistics, as a science, consists of an extremely spread collection of methods and it is divided into two main parts: • Descriptive Statistics • Inferential Statistics and decision-making Each part represents a main step of a statistical research. Descriptive Statistics is a set of techniques used for the description of collectivities (ex. average, structure, movement over a period of time etc). This first stage of statistical treatment of the data aims to describe the common features, the essential issues characterizing a data set in order to obtain as much information as possible. Descriptive Statistics consists of data summarizing, presentation, tabulation, and displaying followed by

Introduction to Statistics

computation of the central tendency measures, analysis of data uniformity, consistency, and symmetry interpretation. Once the data are gathered, the next main purpose of Statistics is to treat them in a specific manner in order to be able to apply further the analysis procedures. Usually this branch of Statistics covers also some aspects of other tools of economic and business research, namely index numbers, time series, correlation and regression. In the modern approach of Statistics, generalizations are made about the whole, which we call population by investigating a portion, which we call sample. Thus, the average income of all families in our country can be estimated from figures obtained from a few hundred families. Such predictions or estimates are generalizations, which we call inferences. The study of how these estimations are made from numerical data is called Inferential Statistics. Inferential Statistics is a set of procedures used to make predictions about the whole population by studying the properties of a population sample. Statistical Inference is gathering the set of methods allowing to: • draw conclusions on a population based on the information characterizing the sample; • forecast the evolution of a phenomenon; • characterize statistical relations between variables. For the overall conclusions drawn - based on a set of data - to be available, the most important condition is for the data set to be large enough and representative, to reproduce the characteristics of the overall set of data. Modern statistical methods are based on the theory of probabilities, allowing the use of partial information (sample data) to produce overall conclusions relative to the large group from which the sample was selected. Statistical theory allows us to make estimates of the population parameters (the arithmetic mean and the standard deviations) based on the sample statistics. When the measures computed from a sample are used to characterize the population, it is necessary to estimate the reliability of the measures, in other words the degree of error to which the generalization may be subject. So we can construct confidence intervals and we can test hypothesis concerning the parameters of the population.

Statistics for Business Administration

There is a large gap between the facts, as they are recorded, and the information, which is useful to the management system, wherever the micro- or macro economic level. The statistical methods enable to reduce this gap and even allow this gap to be bridged. For instance, the management of a plant will know the percentage of defect rates of the fleet of equipments in each branch more effective than the number of defectives. Management generally requires summarized values, which represent large areas, rather than detailed values describing individual instances, which may be untypical.

1.3 Basic Concepts of Statistics Before starting any statistical analysis we need to clarify the main categories used by Statistics. They are forming a set of definitions necessary to be specified at the beginning of any Statistics manual. We will define the terms: population, unit, characteristic and indicator. 1. Population = the total number of elements of the same nature representing the object of the statistical investigation; any finite or infinite aggregation of individuals, not necessarily animate, subject to a statistical study. The term statistical population was initially used to describe the set of people but was developed into an abstract general concept, also known as collectivity. The statistical population, also called general collectivity, overall population or just population, can consist of a set of people, material objects, events, ideas, data. The population (statistical collectivity) represents a collection of all individuals having the same properties. The problem we are trying to solve within a statistical research defines the collectivity. In Mathematics, the population is regarded as infinite. For business and economics we have to consider the population as finite; we have to consider time and space in defining the population. The population can be finite if it comprises a determined number of elements. The finite population can be considered a representative part of the infinite population.

Introduction to Statistics

Examples: 1. Cola consumers in a year are a part of all the possible number of consumers which might have consumed Cola that year. In order to obtain a finite population we need to define its contents, and to locate it in time and space. 2. Last census population in 2002, the definition of the persons comprised within the census was: • considering the content: Romanian citizens located in the country or temporarily abroad during the census • considering its space description: the census comprised the inhabitants all over the country • considering the time delimitation: the data recorded on the census forms referred to the population status at midnight between 2 certain days, even if the data collection period was longer 2. Unit = the basic element of the population, which will be observed within the statistical research. It represents any individual member of a population. The statistical unit is an information vector or the logic subject to be investigated, therefore the need for a precise definition of the statistical unit. The unit is any person or thing, or group of persons and things, regarded as an entity, together constituting the statistical population. We have a simple unit or a complex unit. The units can be simple, as the person, the object, the idea, and complex, as the company, the country, the team, the household. 3. Characteristic (variable) = distinctive peculiarity, trait of the statistical unit, common feature to all the population units, characterizing, describing each unit in a distinguished way. The statistical characteristics can take different values or forms, from a unit to another or, from a group of units to another group. This is because the factors determining the level or the form have different ways of action. Thus, the standard characteristic is variable and it is also called statistical variable. There are many possibilities to classify the statistical characteristics. A first choice can split them according to their contents into three categories: 1.1.Time variables (ex. birthday) 1.2.Territorial variables: shows spatial location of statistical data and units 1.3. Attributive variables – any variable, except time and space

Statistics for Business Administration

According to the second criterium, the attributive characteristics can be classified according to their presentation form into: 2.1. Non-numerical or qualitative, represented by words, also called categories. The qualitative characteristics can also be scalable (can be transformed into numbers according to a scale) and non-scalable (pure nonnumerical). Also the qualitative scalable characteristics can be binary and non-binary, according to the number of possible categories they can take, two or many. 2.2. Numerical or quantitative, represented by numbers. The quantitative characteristics can be: • Discrete, being able to take a finite number of values within an interval of variation, as a result of a counting procedure, like the number of students in a group. Discrete data have distinct values with no intermediate points • Continuous, being able to take an infinite number of values within a variation finite or not finite class, like the oil production measured in barrels Practically every statistical recording is a discrete value, like for instance the river debit. If continuous data would form a frequency distribution, then it would be a continuous frequency distribution. Continuous frequency distributions are more amenable to statistical analysis and most of the theoretical tables are based on continuous values. Because of this fact, in the case of a large statistical population we assume the continuity of data, even though the data are strictly discrete. Some authors consider a third classification criterium for the characteristics, which we considered to be a criterium of classification specific for the qualitative variables: the classification according to the number of values possible to occur. According to this we can have binary variables, with only two possible values and non-binary characteristics, which can take more than two values. Examples of binary variable can be the gender, payment method CASH or NONCASH. 4. Statistics (indicator) = representative measure concerning a statistical distribution for a sample, obtained using numerical calculus from a well and clear defined formula. It is the result of the observation and statistical calculus.

Introduction to Statistics

Other authors do not make the distinction between parameter and statistics. They are using the term indicator instead of measure of any numerical expression obtained using a statistical calculus characterizing a variable. Statistical indicator represents a numerical expression of an economic category. It can concern the structure, the dependences, and the time or space evolution.

1.4 Exercises Multiple choice exercises with answers 1. If in a report we read that for an University the average mark per group of students was 8.77, the statistical population was: a. the student b. the university c. the group d. the groups e. the students ANSWER: d 2. Referring to exercise 1, the statistical unit was: a. the student b. the university c. the group d. the groups e. the mark ANSWER: c 3. Referring to exercise 1, the statistical characteristic was: a. the university b. the average mark per student c. the groups d. the average mark per group e. the mark ANSWER: d

Statistics for Business Administration

4. For a study comprising the number of passengers, number of stops, number of buses, number of controllers the statistical population was made of: a. the buses b. the passengers c. the stops d. the controllers e. there is no statistical population ANSWER: c Multiple choice exercises without answers 5. a. b. c. d. e.

Referring to exercise 4. specify the number of variables: 4 3 2 1 0

6. Which sentences belongs to the Inferential Statistics: a. “The average level of the students at the Statistics exam has decreased over the past years” b. “The average level of the students is continuously decreasing” c. “The average level of students is lower this year compared to the previous year” d. “Based on the past evolution we may expect the level og the students to be lower this year compared to last year” e. After this survey conducted on a representative sample for the students in our University we can conclude that they have an average to high level” 7. a. b. c.

Which sentence belongs to the Descriptive Statistics? Most part of my clients do not prefer to pay in advance Most part of my clients will be extending their orders After studying a sample of major clients we can say that our clients are sending production orders with the value between 3 and 6 millions ROL....