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ECO 154: Introduction To Quantitative Method II is a three unit, one semester ... Write short but explanatory notes on the following sampling techniques.
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CONTENTS
Introduction Course Aims Course Objectives Working Through this Course Course Materials Study Units Textbooks and References Assignment File Tutor-Mark Assignments (TMAs) Final Examination and Grading Course Marking Scheme Presentation Schedule Course Overview How to Get the Most from this Course Facilitators/Tutors and Tutorials Summary
At the end of each unit, you will be required to submit written assignments for assessment purpose. At the end of the course, you will write a final examination.
Course Materials
The major materials you will need for this course are:
There are 24 units in this course as follows: -
Module 1: Basic Introduction Unit 1: Meaning and Relevance of Statistics Unit 2: Types/Branches of Statistics Unit 3: Basic Concepts in Statistics Unit 4: Collection of Data Unit 5: Organization of Data
Module 2: Representation o Data Unit 1: Tables Unit 2: Graphs Unit 3: Charts Unit 4: Histogram and Curves
Module 3: Basic Statistical Measures of Estimates Unit 1: Measures of Central Tendency Ungrouped Data Unit 2: Measures of Central Tendency of Grouped Data Unit 3: Measures of Dispersion Unit 4: Measures of Partition
Module 4: Moment, Skewness and Kurtosis Unit 1: Moments Unit 2: Skewness Unit 3: Kurtosis
Module 5: Basic Statistical Measures of Estimates Unit 1: Basic Concept in Probability Unit 2: Use of Diagram in Probability Unit 3: Experimental Probability Rules Unit 4: Experimental Probability Unit 5: Random Variable and Mathematics of Expectation
Module 6: Index Numbers Unit 1: Meaning and Scope of Price Index Number Unit 2: Weighted Index Number Unit 3: Other Index Number
Textbooks and References
Certain books are recommended in the course. You may wish to purchase or access them for further reading or practices
Assignment File
An assignment file and a marking scheme will be made available to you. In this file, you will find all the details of the work, you must submit to your tutor for marking. The marks you obtain from these assignments will count towards the final mark you obtain for this course. Further information on assignment will be found in the assignment file itself and later in the Study Guide in the section on assessment.
Tutor-Marked Assignments (TMAs)
You will need to submit a specific number of Tutor-Marked Assignment (TMAs). Every unit in this course has a tutor-marked assignment. You will be assessed on four of them, but the best three marks for the best three (that is the highest three of the four marked) will be counted. The total marks for the best three assignments will be 30 percent of your total work.
Assignment questions for the unit in this course are contained in the Assignment File. When you have completed each assignment, send it, together with the Tutor-Marked Assignment (TMA) form to your tutor. Make sure each assignment reach your tutor on or before the deadline for submission. If for any reason, you cannot complete your work on time, contact your tutor to discuss the possibility of an extension. Extension will not be granted after due date, unless under exceptional circumstances.
Final Examination and Grading
The final examination of ECO 154 will be of three hours’ duration. All areas of the course will be examined. Find time to study and revise the unit all over before your examination. The final examination will attract 70 percent of the total course grade. The examination shall consist of questions which reflect the type of self-testing practice exercise and tutor-marked assignment you have previously come across. All areas of course will be assessed. You are advised to revise the entire course after studying the last unit before you sit for the examination. You will also find it useful to review your tutor-marked assignments and the comments of your tutor on them before the final examination.
Unit Title of Work Week’s Activity
Assessment (End of Unit)
Course Guide Module 1 : Basic Introduction Unit 1 : Meaning and Relevance of Statistics Unit 2 : Types/Branches of Statistics Unit 3 : Basic Concepts in Statistics Unit 4 : Collection of Data Unit 5 : Organization of Data
Week 1 Week 1 Week 2 Week 2 Week 3
Assignment 1 Assignment 2 Assignment 3 Assignment 4 Assignment 5
Module 2 : Representation o Data Unit 1 : Tables Unit 2 : Graphs Unit 3 : Charts Unit 4 : Histogram and Curves
Week 4 Week 4 Week 5 Week 5
Assignment 1 Assignment 2 Assignment 3 Assignment 4
Module 3 : Basic Statistical Measures of Estimates Unit 1 : Measures of Central Tendency Ungrouped Data Unit 2 : Measures of Central Tendency of Grouped Data Unit 3 : Measures of Dispersion Unit 4 : Measures of Partition
Week 6 Week 6 Week 7 Week 7
Assignment 1 Assignment 2 Assignment 3 Assignment 4
Module 4 : Moment, Skewness and Kurtosis Unit 1 : Moments Unit 2 : Skewness Unit 3 : Kurtosis
Week 8 Week 9 Week 10
Assignment 1 Assignment 2 Assignment 3
1 2 3 4 5
Module 5 : Basic Statistical Measures of Estimates Unit 1 : Basic Concept in Probability Unit 2 : Use of Diagram in Probability Unit 3 : Experimental Probability Rules Unit 4 : Experimental Probability Unit 5 : Random Variable and Mathematics of Expectation
Week 11 Week 12 Week 12 Week 13 Week 13
Assignment 1 Assignment 2 Assignment 3 Assignment 4 Assignment 5
1 2 3
Module 6 : Index Numbers Unit 1 : Meaning and Scope of Price Index Number Unit 2 : Weighted Index Number Unit 3 : Other Index Number
Week 14 Week 14 Week 15
Assignment 1 Assignment 2 Assignment 3 Revision Week 16 Examination Week 17 Total 17 Weeks
How to Get the Most from this Course
In distance learning, the study units replace the university classroom lectures. This is one of the merits of distance learning; you can read and work through the outlined study materials at your own pace, time and place of your choice. It’s all about the conception that you are reading the lecture rather than listening to it. In the same way that a lecturer might give you some reading to do, the study units contain instructions on when to read your set of books or other materials and practice some practical questions. Just as a lecturer might give you an in-class exercise or quiz, your study units provide exercises for you to do at appropriate point in time. Each of the study units follows a common format. The first item is an introduction to the subject matter of the unit and how a particular unit is integrated with the other units and the course as a whole. Followed by this is a set of objectives. These objectives let you know what you should be able to do at the end of each unit. These objectives are meant to guide you and assess your understanding of each unit. When you have finished the units, you must go back and check whether you have achieved the objectives. If you cultivate the habit of doing this, you will improve your chances of passing the course. The main body of the unit guides you through the required reading from other sources. This will usually be either from your set books or from your course guides. The following is a practical strategy for working through the course. Always remember that your tutor’s job is to help you. When you need his assistance, do not hesitate to call and ask your tutor to provide it. Follow the under-listed pieces of advice carefully:-
statistics addressed include moments, skewness and kurtosis as well as simple probability distribution and price number analysis.
Attention is drawn to the use of simple and lucid statistical issues in solving day to day economic and business related problems. The use of simple instructional language has been adequately considered in preparing the course guide.
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Module 1: Basic Introduction
Unit 1: Meaning and Relevance of Statistics
Unit 2: Types/Branches of Statistics
Unit 3: Basic Concepts in Statistics
Unit 4: Collection of Data
Unit 5: Organization of Data
Table of Contents Introduction Objectives Main Content Meaning and Scope of Statistics Step in Statistical Inquiry Uses of Statistics and Statistical Information Conclusion Summary Tutor Marked Assignment References/Further Reading
The aspect of decision-making that has to do with numerical information is known as Statistics. The word “Statistics” is often used t mean any of the following: numerical information; a summary of numerical information; a discipline. Statistics is generally used to describe a collection of numerical data; for example, population data, health statistics and school enrolment data, among others. It is also used to refer to the summary of a collection of numerical data such as the total, the minimum, maximum, range and average of such data of interest. As a discipline, statistics is the scientific method of decision-making under uncertainty when numerical data and calculated risks are involved. Statistics presents facts in a definite, lucid and concise form so that the facts are readily available for making valid conclusions. Statistics equally synthesizes large mass of data into simple format so that they convey meaning to the reader. The field of study called “Statistics” is fast becoming relevant and essential in all aspects of life because for decision to be appropriately taken, resources judiciously utilized and plans efficiency executed, data has to be collected, organised, analysed and interpreted. These are the bedrock of Statistics.
2.0 OBJECTIVES
At the end of his unit, you should be able to: -
i. Define the term “statistics”. ii. Outline the steps involved statistical enquiry iii. Outline and discuss the relevance of statistics to other fields of study. iv. Identify the limitation of statistics as a tool of decision making.
(i) Problem and the objectives should be properly stated. (ii) Samples should be properly selected without bias. (iii) Questionnaires should be well laid-out. (iv) Data should be collected effectively and efficiently. (v) Data should be properly organized. (vi) Analysis and interpretation of data must be properly carried out. (vii) Outcomes/Results of the analyses should be properly presented. (viii) The report of the inquiry must be presented using simple and illustrative languages such as tables, charts or graphs.
SELF ASSESSMENT EXERCISE 2
Carefully select a social science problem and identify the systematic statistical approach of solving the problem.
3.3 Uses/Relevance of Statistics/Statistical Information
Although statistics is a powerful tool for analyzing numerical data, its application is widely seen in all fields of human endeavour. For instance, we apply statistics to: -
(i) Physical Sciences: - It determines whether or not experimental results should be incorporated into the general body of knowledge. (ii) Biological and Medical Sciences: - Statistics guides the researcher in determining which experimental findings are significant enough to demand further study, or be tested more to meet human needs. (iii) Social Sciences: - The roles of statistics in the social sciences cannot be ignored especially in economics, business and finance. The behaviour of individuals and organizations can be monitored through numerical data. (iv) Engineering: - The professional field of engineering employs statistics in planning establishment policies and strong standards. A civil engineer may use statistics to determine the properties of various materials and perform some durability test. (v) Education: - In the course of teaching, evaluation and assessment, statistics is very essential to analyze performance in examinations. The school headmaster can use statistics to write the curriculum, school enrolments, teachers/staff requirements, staff strength etc. (vi) Meteorology: - Statistical information is also used in meteorology i.e. the science of weather prediction. In fact, the application of statistical techniques is so wide spread and the influence of statistics in our lives and habits is so great that the importance of statistics cannot be over- emphasized.
Apart from the relevance of statistics to the few chosen disciplines (as explained above), the following is the summary of general relevance of statistics in everyday life: -
(i) For summarizing large mass of data into concise and meaningful form leading to a better understanding of condensed data. (ii) Giving visuals impact on data especially when presented in diagram, tables or charts. (iii) Enabling comparison to be made among various types of data. (iv) Making conclusions from data generated in pure experimental, social and behaviour research. (v) Enabling a business establishment to make accurate, reasonable and reliable policies based on statistical data. (vi) Predicting future events in daily life and business. (vii) For the formation as well as testing of hypothesis. (viii) For budgetary planning. (ix) Widely used in industrial and commercial dealings as well as in government establishments. (x) It’s knowledge enables one to understood relevant articles in scientific journal and books
In spite of the relevance of statistics to everyday activities, the field of study (statistics) is limited by the following: -
(i) Statistics data or result is only an approximation of the total and therefore not entirely accurate in some cases. This is because not all the population will be covered for any statistical investigation. (ii) Statistics if not carefully used can establish wrong conclusion and therefore it should only be handled by experts. Where experts are inadequate, some form of training should be conducted for those that may be required to carry out statistical research. (iii) Statistics deals only with aggregate of fact as no importance is attached to individual items.
SELF ASSESSMENT EXERCISE 3
Outline and discuss any five uses of statistics to day to day activities of individuals, firms and the government.
4.0 CONCLUSION
This unit being the first of the introductory has been able to expose you to the meaning and scope of statistics, steps involved in carrying out statistical inquiry as well as the relevance of statistics to different fields of study and the day to day activities.
5.0 SUMMARY
Statistics is generally defined as science of data which involves collecting, classifying, summarizing or organizing, analyzing and interpreting data (numerical information) to be able to arrive at a statistical conclusion. In the course of carrying out statistical enquiry, a number of steps must be
Table of Contents Introduction Objectives Main Content Descriptive of Statistics Inferential Statistics Conclusion Summary Tutor Marked Assignment References/Further Reading
‘Statistics’ means numerical description to most people. Often the data are selected from some larger set of data whose characteristics we wish to estimate. We call this selection process sampling. For example, you might collect the ages of a sample of customers in a video store to estimate the average age or the most frequent age group of the customers in the store. Then, we can use the estimate to target the store’s advertisements to the appropriate age group. It should be noted that statistics involves two different processes: -
(i) Describing sets of data; and (ii) Drawing conclusion (making estimates, decisions, prediction etc.) about the set of data on the basis of sampling.
So, the applications of statistics can be divided into two broad areas: descriptive statistics and inferential statistics.
2.0 OBJECTIVES
At the end of this unit, you should be able to: -
(i) Identify the various branches of statistics. (ii) Explain the various branches of statistics.
3.0 MAIN CONTENT
3.1 Descriptive Statistics
In descriptive statistics , the data collected describes the situation that existed at the point in time when the census was taken. It provides a step by step detail of data available and collected at any given period. The important characteristics of descriptive statistics is that population to be described is definite. Descriptive statistics is the branch of statistics which deals with classification
of data through the drawing of histograms that correspond to the frequency distribution which result after the data representation of data by different types of graphs such as line graphs, bar charts, pictogram, computation of sample mean, median and modes. The computation of variances, means, absolute deviations, deciles, range, percentile etc. are also regarded to as descriptive statistics. The main purpose of descriptive statistics is to provide an overview of the information collected.
Basically, the component of statistical process that deals with the organisation and summarization of information is referred to as Descriptive Statistic. It describes the information collected through numerical measurements, charts, graphs and tables. Therefore, descriptive statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data, and to present the information in a convenient form. Hence, descriptive statistics presents information in a convenient form at usable and understandable form in words with little numerical inclusion in the description of the data.
SELF ASSESSMENT EXERCISE 1
(1) What are the branches of Statistics? (2) What is “Descriptive Statistics”? (3) Outline the various tools used in descriptive statistical analysis.
3.2 Inferential Statistics
Inferential or analytical statistics is the second important branch of statistics. Most often, samples are carefully selected from population. On the basis of the sample, we infer things or conclusion about the population. This inference about populations on the basis of the sample is known as Statistical Inference. In other words, statistical inference is the use of samples to reach conclusions about the populations from which those samples have been drawn. Inferential statistics is mostly linked with probability theory and estimate outcomes of events. Therefore, statistics of inference especially has to do with the measurement of chance.
We usually start with setting up a hypothesis (guess) or a number of hypotheses specifying our assumptions or guesses to be validated or refuted. This is usually stated at the beginning of the study. For example, we can test the hypothesis that the members of PDP are conservative in respect or economic policies while the members of ANPP take literal approach to economic policies. These testable assumptions are made from selected samples of members of the two political parties and not from the entire membership (the population). The result obtained can therefore be used to generalize for the entire political party provided the sampling is unbiased and statistical inquiry is properly carried out. This is technically called statistical inferences.
