# NSU Research Contributions

### Title : STATISTICS FOR BUSINESS, MANAGEMENT AND ECONOMICS

**Authors : **Dr. Md. Sharif Hossain

**Abstract : **For the last three decades or so the use of statistical tools and techniques has been increasing rapidly in different areas of human activity-business, economics, management, banking, finance, agricultural, biology, medicine, psychology, sociology and also other disciplines in social and natural sciences. It is now generally accepted in all societies that study of modern business, economics and management is incomplete without a proper knowledge of statistics. In view of the increasing complexity and variety of problems in the field of business, economics and management, a student without a fair knowledge of statistical methods and techniques may not be able to cope, and hence may remain unfamiliar, with many aspects of business, economic and managerial problems. Thus the book, “Statistics for Business, Management and Economics” is written for the students in basic and applied statistics courses in business, economics, management and other social sciences as well as for the researchers already engaged in these fields who desire an introduction to statistical methods and their application. In writing the first edition of this book, my aim is to offer the students a balanced presentation of fundamental statistical concepts and methods along with practical advice on their effective application to real-life problems. This book covers almost all aspects of statistical techniques with giving priority on inferential statistics-probability theory, probability distribution, sampling distribution, statistical estimation, and testing of statistical hypotheses, including a large number of nonparametric tests. It also includes topics of correlation analysis, simple and multiple linear and nonlinear regression equations, analysis of time series, analysis of variance and index numbers. This book is organized into twenty chapters and discussed below in briefly:
In chapter one meaning of statistics and business statistics, scope and limitation of statistics also some important statistical methods are discussed to collect primary and secondary data. In chapter two, some important techniques are discussed to present and organize numerical data in a systematic, scientific and proper manner. Also different fundamental notations which are widely applicable for statistical analyses of numerical data are also presented in this chapter. In chapter three, different measures of central tendency are discussed to describe numerical data by using only a single number. Some important mathematical properties of different measures of central tendency are also presented in this chapter. In chapter four, different measures of dispersion are presented which deal with about how the individual observations are distributed around the mean value of frequency distributions. Some important mathematical properties of different measures of dispersion are also presented in this chapter. Two most important characteristics namely measures of central tendency and measures of dispersions do not completely describe a frequency distribution. In order to describe a frequency distribution completely one more characteristic is essential: the shape of the distribution. There are two kinds of shape characteristics namely asymmetry and peakness of a frequency distribution. More specifically, these are called skewness and kurtosis. Measures of skewness summarize the extents to which the observations are symmetrically distributed. Measures of kurtosis give the idea of peakness of a frequency distribution. Different measures of skewness and kurtosis are described in chapter five. Some important theorems that are associated with different measures of skewness and kurtosis are also presented in this chapter.
Sometimes we have to face an uncertain situation for solving different types of business, economic and managerial problems. A most popular and commonly used mechanism to deal with this uncertain situation is known as the probability theory. In chapter six different fundamental concepts which are most popular and widely applicable in probability theory are discussed. The set theory which is closely related with probability theory is also discussed in this chapter. Probability distribution is one of the important concepts in probability. The students can understand the concept of probability distribution by first getting the idea of a random variable. The concepts of random variable and probability distribution of random variables are discussed in chapter seven. Also in this chapter different measures of central tendency and dispersion are introduced in case of discrete and continuous random variables. In chapter eight several discrete probability distributions which are widely applicable for solving different types of business, economic and managerial problems namely; (i) uniform distribution, (ii) Bernoulli distribution, (iii) binomial distribution, (iv) negative binomial distribution, (v) geometric distribution, (vi) multinomial distribution, (vii) hypergeometric distribution and (viii) Poisson distribution are discussed with their important characteristics. In chapter nine the most popular and widely applicable continuous probability distributions namely, (i) uniform distribution, (ii) gamma distribution, (iii) exponential distribution and, (iv) normal distribution are discussed with their important characteristics. We know every statistic is a random variable because its value varies from sample to sample. The probability distribution of any statistic is called sampling distribution. In chapter ten, sampling distributions of different statistics such as sample mean , difference of two sample means, sample proportion p, difference of two sample proportions are discussed for both cases with and without replacement. We know estimation is a most popular and widely used technique to find the answer of a particular question regarding population parameters based on the sample observations. In chapter eleven some important concepts of estimation, different estimation techniques and interval estimations of different population parameters are discussed. Different important characteristics of a good estimator are also discussed in this chapter. One of the most important techniques of making statistical inference about the population parameter(s) or about the form of the population distribution is of testing statistical hypotheses. In chapter twelve different important concepts in hypothesis testing and also different techniques of testing statistical hypotheses about population parameter(s) such as test concerning population mean(s), population proportion(s), population correlation coefficients, and population variance(s) are discussed.
In this book, different topics that are discussed from chapter one to chapter twelve are associated to the analysis of univariate data that is the data on a single variable. But in practice, different problems in the field of business, economics, finance, marketing, banking, medical sciences as well as in natural sciences there exists relationships between two or more than two variables which should be widely applicable of decisions making or policy formulation. Correlation analysis is one of the most important techniques to study the relationship between two or more than two variables. Therefore correlation analysis is discussed in chapter thirteen. We know most of the research problems in the field of business, economics, finance, banking, management, medical sciences as well as in natural sciences etc are associated to the topic of modeling i.e. try to describe how the dependent and independent variables are related to each other. Thus to explain these types of relationships, in chapter fourteen simple linear and non-linear regression models are discussed and also has been shown how to fit them to a set of data points using different methods namely method of least squares, maximum likelihood method, and method of moments etc. It has also been shown how to judge whether a relationship between a dependent variable (y) and independent variable (x) is statistically significant, how to use the model to estimate expected value of y, and to forecast a future value of y for a given value of x. In this chapter, proper justifications for the techniques employed in a regression analysis are also provided and in chapter fifteen multiple linear and non-linear regression techniques are discussed to show how the dependent variable is influenced by several independent variables. Also in this chapter the assumptions underlying classical multiple linear regression models and also the OLS and ML methods for estimation of multiple regression equations are discussed. In chapter sixteen, three most popular and widely used experimental designs namely completely randomized design (CRD), randomized block design (RBD), and Latin square design (LSD) are discussed in order to test the null hypothesis of equality of several treatment means. In hypothesis testing, when inferences are made about the population’s means, it is necessary to assume that the sample is drawn from the approximate normal population. But in practice, most of the business and economic problems do not satisfy the assumption of normality. Therefore, in chapter seventeen, different techniques for making statistical inferences about the shape of a population distribution or populations’ means are discussed which are not based on the assumption of normality of the population from which the independent and random sample is drawn. In this chapter at first, techniques for testing hypothesis about the form of the population distribution whether a sample is drawn from a binomial, a Poisson, a normal or some other distributions are discussed and then some techniques are discussed for comparing two or more populations’ means that are based on the ordering of the sample observations according to their relative magnitudes. In this chapter the chi-square test for independence of two attributes, and for testing homogeneity of k independent samples are discussed. Also the most popular nonparametric tests that are widely applicable in business, economic and managerial problems such as (i) one sample sign test for mean or median, (ii) two sample sign test of paired observations for the difference of two means or medians, (iii) one sample Wilcoxon signed-rank test for mean or median, (iv) Wilcoxon signed-rank test of paired observations for the difference of two means or medians, (v) Wilcoxon rank-sum test for independent samples, (vi) Mann-Whitney U test for independent samples, (vii) Kruskal-Wallis H test, (viii) test of randomness and (ix) median test are discussed. In the field of business, economics, banking, finance and management etc, forecasting is commonly used for appropriate timely decision making and policy formulation in respect of different problems. Forecasting cannot be done unless data representing changes over a period of time are systematically and scientifically analyzed. Thus in chapter eighteen different techniques are discussed to analyze time series data. We know continuous changes are occurring in prices, output level, sales revenue, cost of living, wages, investment, exports, imports, profits, population, unemployment, industrial activities, business conditions, health and academic standard, etc. The index number is most popular and widely used technique to measure average change of a group of related variables over two different time periods or two different situations which enable us to arrive at a single representative part. Thus in chapter nineteen several methods for constructing unweighted index numbers such as (i) simple method, (ii) simple aggregate method, and (iii) simple average of relative method and also for constructing weighted index numbers several methods such as, (i) Laspeyre’s method, (ii) Paasche’s method, (iii) Dorbish and Bowley’s method, (iv) Fisher’s method, (v) Marshall- Edgeworth method, and (vi) Kelly’s method are discussed. Finally in chapter twenty, constrained and unconstrained optimization techniques are discussed for solving different types of single variable and multivariable business, economic and managerial problems.
The subject matter in each chapter has been discussed with solved real-life problems so as to enable the students to have a better understanding and appreciation of the application of different statistical methods. Large number of questions and problems are given at the end of each chapter to assist the students for understanding concepts and to enable students to obtain experience in applying statistical methods in practical situations and interpreting results of statistical investigations
In my efforts to complete this book, I have been greatly helped by a large number of colleagues and friends. It is to be mentioned here that I am very grateful to my collegues and friends Kawser Jahan, Dr. Belal Hossain, and Mohammad Riazuddin Molla, who read through parts of the manuscripts and provided me with comments and suggestions. I am also greatly indebted to Mullick & Brothers and its owner Kamrul Hasan Mullick, for taking special care towards the publication of this book. Finally I want to thank my wife Lutfun Nahar (Lata) and my two children Feeha and Farha for their patience and encouragement for all the times that my mind was with this book when it should have been with them

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Year : November, 2014 |
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Pages : 934 |
City : Dhaka |
Edition : First |
Editors : Professor Dr. Md. Sharif Hossain |

Publisher : Mullick & Brothers |
ISBN : 978-984-33-8276-4 |
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