Unit I
Business Statistics
1.1.1 Introduction of Statistics:
The word statistics is derived from the Latin word “Status” that means a group of numbers that represent some information of our human interest. In ancient periods, the use of statistics was made to meet the administrative needs of the state. In modern time, the statistics is not only used for administrative of the state alone, also evaluate all those activities in our lives which can be expressed in quantitative terms.
The term “statistics” is defined in two senses: - in singular and in Plural senses.
Firstly, in plural sense, statistics means systematic collection of numerical facts. Secondly in singular sense, the term statistics means the various methods used for collection, analysis and interpretation of numerical facts. It is described as statistical method. In our study we are more concerned with the second meaning of statistics.
1.1.2 Definition of Statistics:
“Statistics is a body of methods for making wise decisions on the face of uncertainty.” —Wallis and Roberts
“Statistics is a body of methods for obtaining and analysing numerical data in order to make better decisions in an uncertain world.” —Edward N. Dubois
Statistics are numerical statement of facts in any department of enquiry placed interrelation to each other. - Bouly.
The science of Statistics is essentially a branch of applied mathematics and can be regarded as a mathematics applied to observation data. - R.A fisher.
After analysing the various definitions of statistics, the most proper definition of statistics is as follows –
“Statistics in the plural sense are numerical statements of facts capable of some meaningful analysis and interpretation, and in singular sense, it relates to the collection, classification, presentation and interpretation of numerical data.”
1.1.3 Scope of Statistics:
1.1.4 Functions of Statistics:
Expression of facts in numbers – One of the important function of statistics is to express facts in definite form ie, in the form of numbers. The results expressed in definite form are more convincing than the result expressed on the basis of quality.
Presentation of facts – Statistics helps in presenting the complex data in a simple form, so that it becomes easy to understand. Statistical methods present data in the form of graph, diagram, average, coefficient, etc.
Comparison – After simplifying the data, it can be correlated and compared. Comparing data relating to fact is one of the functions of statistics as absolute figures convey less meaning.
It helps other science- Many laws of economic, law of demand, law of supply has been verified with the help of statistics.
Forecasting – Statistics also predicts future course of action. On the basis of estimates with the help of statistics we can make future policies.
Policy making – Statistics helps in formulating favourable policies. Based on the forecast the government makes policies.
1.1.5 Importance of Statistics:
Importance for administrator administration – With the help of statistics, finance minister makes the use of revenue and expenditure data to prepare budget. Also, it helps in taking decision regarding taxes.
Importance for businessman – statistics helps in providing relevant data. Thus, with the help of those data a business man can estimate demand and supply of the commodity.
Importance in economics – statistics helps in measuring economics such as gross national output, consumption, saving, investment, expenditures, etc.
Importance for politician – Politician use statistics in formulating economic, social and educational policies of the country
Importance in the field of education – statistics has wide application in education for determining the reliability and viability to a test, factor analysis, etc.
1.1.6 Limitations and Distrust of Statistics:
Study of numerical facts only – statistical method does not study quantitative phenomena such as honesty, wisdom, etc. So experiments are done to measure the reaction of man through data.
Study of aggregates only – statistics study only aggregates of quantitative facts. It does not study any particular unit.Prof. Horace Sacrist defined statistics, “By statistics we mean aggregates of facts…. And placed in relation to each other”
It does not depict the entire story of phenomena – Any phenomena happen, due to many causes. But all the cause is not expressed in numbers. So, correct conclusion cannot be drawn. Analysing quantitative data and ignoring qualitative data cannot give 100% conclusion.
Homogeneity of data – To compare the data, it is essential that whatever statistics are collected, the same must be uniform in quality.
It is liable to be miscued – As W.I. King points out, “One of the short-comings of statistics is that do not bear on their face the label of their quality.” Thus, the data collected by inexperienced person may be dishonest or biased. So, to get correct conclusion data must be used in caution.
Too many methods to study a problem –to find a single result many statistical methods are used. All the methods result vary in each case. “It must not be assumed that the statistics is the only method to use in research, neither should this method of considered the best attack for the problem.” —Croxten and Cowden
There are various method of statistical methods which can be broadly classified into five types as thus:
- Descriptive methods
- Analytical methods
- Inductive methods
- Inferential methods
- Applied methods.
Descriptive Methods
This type of method consists of all the preliminary steps to final analysis and interpretation. This method includes the method of collection, methods of tabulation, measures of central tendency, measures of dispersion, measures of skewness, and analysis of time series. These methods find out the various characteristics of data and help in summarising and interpreting the salient features of the data. This method is also called as descriptive statistics.
Analytical Methods
This method includes all those methods which help in the matter of analysis and comparison between any two or more variables. This includes the methods of correlation, regression analysis, association of attributes and the like. This method is also called as analytical statistics.
Inductive Methods
This type of method consists of all those procedures that help in the generalization or estimation over a phenomenon on the basis of random observation or partial data. This includes the procedure of interpolation, extrapolation, theory of probability and the like. This methods is also called as inductive statistics.
Inferential Methods
This type of method consists of those procedures which help in drawing inferences about the characteristics of the population on the basis of samples. As such, this method includes the theory of sampling, different tests of significance, statistical control etc. This method is also called as inferential statistics.
Applied Methods
This type of method consists of those procedures which are applied to the problems of real life. This includes the method of statistical quality control, sample survey, linear programming, inventory control and the like.
Definition
Data collection is defined as the procedure of collecting, measuring and analyzing accurate insights for research using standard validated techniques.
Irrespective of the field of research, data collection is the primary and most important step for research. Depending on the required information, the approach of data collection is different for different fields of study.
The objective of data collection is ensuring that rich information and reliable data is collected for statistical analysis so that data-driven decisions can be made for research.
Data collection method
Data collection methods can be divided into two categories: secondary methods of data collection and primary methods of data collection.
Secondary data - Secondary data is a type of data that has already been published in books, newspapers, magazines, journals, online portals etc. there is lot of information available in these sources. Therefore appropriate secondary data are used in the study plays an important role in terms of increasing the levels of research validity and reliability.
Primary data –
Primary data collection methods can be divided into two groups: quantitative and qualitative.
Quantitative data collection methods are based in mathematical calculations in various formats. Methods of quantitative data collection and analysis include questionnaires with closed-ended questions, methods of correlation and regression, mean, mode and median and others. Quantitative methods are less expensive and they can be applied within shorter duration of time. These methods are easy to make comparison between the findings.
Qualitative research methods, on the other hand, do not involve numbers or mathematical calculations. Qualitative research is closely associated with words, sounds, feeling, emotions, colours and other elements that are non-quantifiable.
Primary and secondary data are discussed more in detail in the below section.
1.4.1 Primary Data:
Primary data is the information collected through original or first-hand research. Primary data is more reliable and authenticate as the data is nor changed or altered by any human beings. Also, the data is not published yet. Primary data is gathered by any authorized organization, investigator, and enumerator.
“Data which are gathered originally for a certain purpose are known as primary data.” — Horace Secrist
Sources of primary data
The sources of primary data are as follows –
1. Experiments: In natural sciences, experiments are most reliable source of data collections. Experiments are conducted for medicine, psychological studies, nutrition and other scientific studies. Experiments are conducted in the fields as well as laboratories. The results of experiments are analysed by statistical test and thereafter conclusions are drawn.
2. Survey: surveys are used in social science, management, marketing and psychology to some extent. Surveys are conducted in different methods.
3. Questionnaire: Questionnaires consist of list of question either open ended or close ended for which the participants answer. Questionnaire can be conducted via telephone, mail, institute, fax, etc.
4. Interview: Interviews are expensive method of data collection. The interviewer collects information from each respondent independently. It involves in-depth questioning and follow up question. While taking interview, the interviewer can observe the body language and other reaction to the question.
5. Observation: observation can be conducted with or without knowledge of the participants. Observation can be made either natural or artificially created environment.
Advantages
1. Date interpretation is better – depending on the need of marketers, the data collected are examined and interpreted properly rather than relying on secondary data.
2. Efficient spending for information – Under primary research, the data collected specially for the purpose in mind. So, the research funds are used efficiently unlike secondary research where marketer spent for information that is not needed.
3. Proprietary issue – information from primary research is their own and is not shared by any others. The information can be kept hidden from the competitors and also give added advantage from competitors who rely on secondary data.
4. Addresses specific research issue – primary research helps the marketers in getting that information which they want to know and report it in ways that benefit them. While information from secondary research may not fit the need of marketers.
5. Greater control – primary research not only focus on specific issue; it also enables the marketers to have greater control over the information collected. Such as location, time for completing project, etc.
Demerits
1. High cost – primary research is very expensive compared to secondary research. It involves high expenses in preparing, designing and carrying out the research.
2. Time consuming – primary research starts from deciding to undertake a research project to the end point of having result is very time consuming compared to secondary research which can be collected in less time.
3. Inaccurate feedbacks – primary research involves taking feedback from target audience. There are high chances that feedback given is incorrect, as the audience can be biased or just give for sake of it.
4. More number of resources required – the data is collected from other resources like human resource, material which are needed in large quantity to do the survey. Also, the data are collected from skilled person only.
1.4.2 Secondary Data:
Secondary data are public information that has been collected by others. The data collected from primary research and used by other is referred as secondary data. The secondary data may be obtained from various sources like industry surveys, database and information system, etc.
“The data which are used in an investigation, but which have been gathered originally by someone else for some other purpose are known as secondary data.” — Blair
Sources of secondary data
Government statistics – government statistics are widely available and easily accessible online. It provides information regarding trade activity, pricing and economic trends, business information, patents, population statistics, heath record, etc
Books – books are available on any topic you want to research. Books provide insight on how much information is given for a particular topic and you can prepare your literature review.
Journals – journals provide up to date information on the very specific topic on which you want to research. Journal is one of the most important sources for providing the information on data collected.
Magazine or newspaper – Newspaper or magazine provide daily information regarding politics, business, sports, fashion, etc which can be used for conducting research.
Internet – internet is becoming advance, fast and reachable to the masses and much information is available on internet. Almost all journals, books are available on internet. Some are free and others you have to pay price
Company website – company’s website provides lots of information. They have a section called investor relations which contains full of annual reports, regulatory findings and investor presentations that can provide insights into both the individual company’s performance and that of the industry at large.
Advantages
1. Ease of access – Secondary research is easily available. In past secondary data was available in libraries or wait for the reports to be shipped. Currently, the data are available online and can be accessed any time.
2. Low cost to acquire – the researcher can get information at very low cost compared to carrying out research themselves. Time and money is saved in secondary data.
3. Clarification of research question – The use of secondary data helps in clarifying the research question. Sometimes secondary researches are done prior to primary research to clarify the research focus.
4. Difficulties in conducting primary research – sometimes primary research is difficult to be conducted due to time, cost, etc. Thus, secondary data are used to carry out the research and accordingly the results are drawn.
Disadvantages
Quality of research – primary researches are conducted and controlled by the researcher. Thus, it ensures the validity of the information. While secondary researches are conducted by others. Thus, the viability and reliability of the secondary data are questionable.
Not specific to researcher needs – in many cases, secondary research does not meet the researcher’s needs. While primary research gets information the way researcher wants.
Incomplete information – In many cases, researcher provide few information. To get the full version of the report they charge expensive fees.
Not timely – while using secondary research, the researcher should check the date of information. Sometimes out of date reports are available which is not relevant to the current market situations.
A graph is a visual form of presentation of statistical data. A graph is more attractive than a table of figure. It helps the common man to understand more efficiently and effectively. It facilitates comparisons between two or more phenomena very easily.
Histogram – histogram is a bar graph representing the frequency of occurrence by classes of data. In histogram data are plotted as a series of rectangle. ‘X axis’ consist of class intervals and ‘Y axis’ shows the frequencies. It is also called stair case or block diagram. Histogram is not suitable for open ended classes.
Frequency polygon –a frequency polygon is a graph where midpoints of each interval are joined by using lines. The heights of the points represent the frequencies. It is usually done by creating a histogram or by calculating the midpoints of each interval from the frequency distribution table.
Frequency curve – a frequency curve is a smooth curve obtained by joining the midpoints of all rectangles forming histogram. It is drawn by using free hand. The curve should begin and end at the base line.
Ogive – An ogive graph shows cumulative frequency in statistics. It estimates the number of observations less than a given value or more than a given value. Cumulative frequency is obtained by adding to the given value
Less than ogive method - The frequencies of all preceding classes are added to the frequency of a class.
More than ogive class - The frequencies of the succeeding classes are added to the frequency of a class
Lorenz curve – It is the graphical representation of income and wealth. It was developed by Max O. Lorenz in 1905. The Lorenz curve shows how wealth, revenue, land, etc are not equally distributed among the people.
