Module of Statistics and Probability
1. Module Code: MATH 218 Faculty: Education
2. Module Title: Statistics and Probability
3. Level: 2 Semester: II Credits:3
4. First Year of Presentation: 2018-2019. Administering Faculty: Education 5. Pre-Requisite: Descriptive Statistics and Applied Math
Course Instructor: Dr. Rosa Padilla de Casamayor
Course Website: https://sites.google.com/a/upeu.edu.pe/rosa-padilla/ Course Venue/Time: Wednesday 08 – 11:00
Consultation Time: Thursday 8:00 – 12:00. At professor’s office
6. ALLOCATION OF STUDY AND TEACHING HOURS:
No Criteria Student hours Lecture hours
1 Lectures 25 50
2 Seminar /workshops 10 10
3 Practical
classes/Laboratory(computer LAB for statics software)
20 40
4 Structured exercises 25 10
5 Set reading 20 5
6 Self directed study 25 2
7 Assignments-preparation and
writing 20 8
8 Examination & participation 5 15
Total student hours 150 140
7. DESCRIPTION OF AIMS AND CONTENT
Course is theoretical-practical, belongs to the area of science. The course covers the fundamental tools and features for descriptive statistics, probability and statistical inference, and demonstrate real world applications, particularly such linked to the field of Education. It covers the following topics: Data gathering, organization and presentation of data, measures of central tendency and measures of variability; Probability and Probability Distribution, Discrete probability distributions: Bernoulli, Binomial, Hypergeometric and Poisson distributions, and continuous distributions of random variables: the Family of Uniform Probability Distribution, Normal Distribution and Standard Normal Probability Distribution. Estimation, Margins of Error and Estimates, confidence intervals and hypothesis testing. Analyze dataset using Window Excel and Statistical Package for Social Sciences SPSS v 25.
Learning Outcomes
8. Student Learning Outcomes/Objectives
Upon successful completion this course, the student will be able to: 8.1 Knowledge and understanding:
Use probability and statistics to analyze real-world situation
Understand the logic of statistical inference and will be able to apply common inferential procedures.
Analyze real-world scenarios and determine the appropriate type of statistical analysis according to the research objectives and the type of variable.
8.2 Cognitive-intellectual-application of knowledge:
Apply appropriate methods to collect data and construct, interpret and evaluate data visualizations, including different types of graphs according to the type of variable, particularly those related to the economics field and two-way tables.
Utilize graphical and numerical summaries of data in understanding data generating processes. Apply your understanding of various statistical terms and methods for summarizing, organizing, and
presenting data.
Compute and Use measures of central tendency, position, and variability, interpret them and apply in the real context.
Apply knowledge of probability and probability distributions to solve real problems. 8.3 Communication-ICT-Analytic Techniques-Practical Skills:
Set up data, from a suitable quantitative study, for data analysis through the use of calculators, spreadsheet programs (Excel) or special purpose data analysis packages (SPSS)
Interpret the output of the statistical software
Sample exams are posted in course website (https://sites.google.com/a/upeu.edu.pe/rosa-padilla/) I highly recommend that you work on the sample exams and discuss the answers with your groupmates/classmates.
8.4 General Transferable Skills:
Upon successful completion this course, the student will be able to:
Use basic counting techniques (multiplication rule, combinations and permutations) to compute probability and odds.
Use Excel and SPSS to run basic simulations of probabilistic scenarios.
Set up and work with discrete random variables. In particular, understand the Bernoulli, binomial, geometric and Poisson distributions.
Describe sample space and events and demonstrate their knowledge of various counting techniques, notions of probability, random variables and various discrete and continuous probability distributions.
Strengthens Christian worldview through various curricular, co-curricular and social projection developed during the semester.
9. Course Content
Unit 1. Exploring Univariate Data
Week Date Objectives [LearningCapabilities] Contents to study in classroom classroom (Assignments)Learning outside the
1. 13/01
Data are accurately presented using all appropriate
tables/graphs/numerical measures with proper labels/titles and correct interpretations
Review of Syllabus and course requirements. Relationship between statistics and probability. Data gathering, organization and
presentation of data. Course project (analysis and write up of a data set. Must be approved by lecturer)
List the reasons for studying statistics and probabilities. Download Chapter I of the lecture notes (posted on the course website).
Work the project in groups of three; the project will be submitted on the 14th week
2. 23/01 Use basic terminology for describing data. Explain the concept of
Measures of central tendency (Mean and Median) and measures of variability (standard deviation,
Central Tendency and Variability
Range).
Course project (analysis and write up of a data set. Must be approved by lecturer)
Visit the web page of http://www.statistics.gov.rw/, so you can surf to get the economic information that you need for assignment 1. Work the project in groups of four; deliver on the date 05/12
3. 30/01
Use Excel and SPSS to obtain descriptive statistics and visual report such graphs and interpret the output.
Quiz 1
IQR and Finding Outliers Graphs and Describing Distributions. An introduction to SPSS software and Excel. Bring your laptop (if you have one) to class. Make sure that SPSS is installed on your laptop.
Continue solving the
assignment 1, and solve quiz 1
Use excel and SPSS to prepare an appropriate type of graph and descriptive analysis
Unit 2. Introduction to Probability and Bivariate data
Week Date Objectives [LearningCapabilities] Contents to study in classroom
Learning outside the classroom (Assignments)
4. 06/02
Identify and Apply the appropriate approach to assigning probabilities. Calculate probabilities using rules with correct
interpretation.
Probability: What is probability? Definition (classical, empirical and subjective probability). Rules of addition and multiplication.
Experiment, Sample Space, Event.
Download Chapter II of the lecture notes (posted on the course web site).
Solve assignment 2, is located on the course website.
5. 13/02 Calculate probabilities using contingency tables and tree diagrams
Contingency Tables and Probabilities. Conditional.
Computing conditional probabilities. Tree Diagrams
Continue solving assignment 2
6. 20/02
Mid Term answers
individually with honesty and criterion.
Determine the number of outcomes using the appropriate principle of counting. .
Evidence knowledge of the subject and Applies to real life problems.
Mid-Semester examination. Covers all material covered to date. Bring your student ID.
Counting Techniques, Combinations and Permutations.
Sets and Venn Diagrams. General Probability Rules
The feedback is very important in the
process of teaching and learning, it is why the student has the opportunity to review their examination after being evaluated.
Unit 3. Discrete and Continuous Probability Distributions
Week Date Objectives [LearningCapabilities] Contents to study in classroom Learning outside theclassroom
7. 27/02
Identify the characteristics of a probability distribution. Compute the mean and the standard deviation of a probability distribution
What is a probability distribution? Chance processes, expected value, chance errors, standard error. Random variables: Discrete and Continuous. The Mean, Variance, and Standard Deviation of a Probability Distribution
Download Chapter III of the lecture notes (posted on the course web site).
Solve assignment 3, is located on the course website.
8. 06/03
Distinguish between a discrete and a continuous random variable. Describe and compute probabilities for a Binomial distribution
Quiz 2
Discrete probability distributions: Bernoulli and Binomial distribution. Applications.
Continue solving assignment 3 and solve quiz 2
9 13/03
Describe and compute probabilities for
Hypergeometric and Poisson distribution
Hypergeometric and Poisson distributions. Application in economics problem
Continue solving assignment 3
10 20/03 Characteristics of continuousprobability distribution Some properties, Kolmogorov definition, Random number generation. Application
Continue solving assignment 3
11 27/03
List the characteristics of the Normal distribution. Convert a Normal Distribution to a
Introduction. The Family of Uniform Probability Distribution. The Family of Normal Probability Distribution.
List the characteristics of the Uniform
Standard Normal
Distribution. The Standard Normal Probability Distribution.
normal distribution to solve economic problems.
Unit 4. Central Limit Theorem. Estimation and Confidence Intervals. Hypothesis
Week Date Objectives [LearningCapabilities] Contents to study in classroom Learning outside theclassroom (Assignments)
12 03/04
Understand the concept of sampling distributions and estimation. Explain the Central Limit theorem
Quiz 3
Sampling Distribution of mean and proportion. The Central Limit Theorem.
Introduction to Parameter Estimation. Point Estimate for a population mean. Confidence intervals for a population Mean and Proportion
Download Chapter IV of the lecture notes (posted on the course web site).
Solve assignment 4, is located on the course website. Submissions and defense of the project in class Genocide
13 17/04
Comprehend the basic concepts used in testing statistical hypotheses. Explain the five-step hypothesis-testing procedure.
Statistical Inference about Means and Proportions with a single Population. Five-Step Procedure for Testing Hypothesis
Conduct and correctly interpret t tests for a single population. Continue solving the assignment 4
14 24/04 Application of the course through the course project Delivery and presentation of the project of the course applied to statistics and probabilities
Presentation of the course project in hard and soft copy
15-16 01/04
The purpose of taking the final exam is that the students demonstrate their knowledge of the subject matter and as applied and evaluates the results.
Final Exam. Covers all material since the beginning of the course. Bring your student ID, pencil.
The feedback is very important in the process of teaching and learning, it is why the student has the opportunity to review their examination after being evaluated.
10. Methodological Strategies [Learning and Teaching Strategies] In the development of the subject will use the following methodology:
Theoretical class: Exhibition will include a first stage, and then develop constructive learning with student participation, to strengthen cognitive contents.
Group dynamics: Students form groups to solve exercises and problems programmed for this purpose. After submitting their report, will be the exposure of results obtained, so that reinforce cognitive content, procedural and attitudinal also the respective feedback.
Individual work: Application Development Course exercises in the specialty outside the classroom.
Consulting teacher: Guidance and counseling teacher for clarification of doubts and assistance in carrying out their assignments.
The Course Project: The student will analyze a data set, demonstrating mastery of the concepts and techniques learned in the class. The data can come from a source available to the student or may be obtained from the Instructor. In either case, the data must be pre-approved by the Instructor. Details of the project will be given during the course.
Topic Objective
To learn about and understand some important statistics about Rwanda and how it is improving.
To understand how statistics can vary across the districts, gender, age groups and different income groups.
Topic example:
Poverty by district – Rwanda 2012 - 2017 Questions and Sample Answers Poverty:
When families don’t have enough money to provide for the things they need to live a healthy life, like food, housing, and medicine.
Q1. What are the districts with the highest poverty rate?
Q2. What is the district with the lowest rate of poverty?
Q3. Why do you think some districts are doing better than other districts?
Q4. What would you like to see change in your community to improve people’s standard of living?
Q5. With the statistical data that you investigate in your project, you can apply the theory of probability learned and find some probability for your research topic.
Net attendance rate in primary school
Q1. Show true the appropriate graph the percentage of students attending primary school between 2002 to 2018
Q2. Why do you think the percentage of students attending primary school has increased over the past 15 years?
Q3. What do you hope to see happen over the next 15 years for primary education attendance? Possible student question: “Why did the percentage decrease by 2% from 2010 to 2013?” Child malnutrition (under 5) by district
In 2014/2015, more than 42% of children under 5 years old in ten districts were stunted (RDHS) Q1. What does malnutrition mean?
Q2. What is the district with the highest level of malnutrition? Q3. What is the district with the lowest malnutrition?
Q4. Why do you think some districts show higher malnutrition?
Literacy rate of the population 15-24 (%) according to wealth quintile Q1. What does literacy mean?
Q2. Is there a pattern between how much a family spends and if their children can read and write? Q3. What do you notice between 2010 and 2015 for both richer and poorer families?
Q4. Why do you think the literacy levels increased between these dates for both rich and poor households?
Fertility rate
Rwandan families today have fewer children, and as a result, children enjoy more attention and care from their parents (RDHS).
Q1. Why do you think the number of children mothers are having has decreased? Q2. Why might fewer children be better for families?
Q3. What may the number of children born per mother be in 15 years’ time?
The Millennium Development Goals relationship with the with the Sustainable Development Goals of Rwanda.
Integration Activities
Making decisions based on Christian principles axiological. Daily Bible Study (Sabbath School lesson)
Using biblical references in academic
Student Conduct (Rules according to Academic policy)
Attendance: If you miss the first day of class or any two consecutive classes after that without communicating with the teacher, you may be dropped. Attendance is recorded every class period. Statistics and Probability is a cumulative subject and each class builds on the previous class' material. The students, who, because of excessive absences, cannot complete the course successfully, are required to be administratively dropped from the class at midterm. Do not stop attending and assume that you will be withdrawn from the class by the teacher.
The student is responsible for all assignments, changes in assignments, or other verbal or written information given in the class, whether in attendance or not.
Academic Honesty: A student who cheats, plagiarizes, or furnishes false, misleading information to the University is subject to disciplinary action up to and including failure of a class or suspension/expulsion from the University.
Class Participation: Participation in class involves demonstrating an interest in the reading material and sharing insights with others in class discussion and group exercises.
Cell Phones: To be turned off while in class.
Respect: Each person in this classroom comes from a different place, has experienced different things and is unique. This classroom will have a positive educational environment where we can learn from each other and grow intellectually. Treat everyone in the classroom with courtesy and respect.
Food, Drink (except water), and Gum chewing – not permitted in the classroom.
11. ASSESSMENT STRATEGY
Assessment is a necessity in teaching otherwise the learner cannot take this process as a serious thing. According to AUCA internal regulations, Continuous Assessment Tests (CAT) is composed of four parts, which composed of 70% of the grade and the Final Exams 30% as reflected in the assessment pattern table.
12. ASSESSMENT PATTERN
Component Weighting (%) Learning Objective Covered
CAT
Class active participation 10 All Objectives
Course project (analysis and write up of a data set, must be approved by lecturer)
10 Objectives 8.1; 8.2 ; 8.3.2; 8.4
Quizzes and assignments 20 Objectives 8.1.1; 8.1.2
Mid-semester exam 30 Objectives 8.1.2; 8.1.3; 8.1.1
Final examination 30 Objectives 8.1; 8.3
Total 100
13. STRATEGY FOR FEEDBACK AND STUDENT SUPPORT DURING THE MODULE
The feedback will be done at the beginning of each class. We will also invest time discussing about the quizzes, assignments and answering the questions and doubts during the classes.
The students may consult and will be supported to clarify about the topics addressed in class or about the assignments; nevertheless, the consultations should be done at the professor’s offices in Masoro Campus.
14. INDICATIVE RESOURCES
Core Texts (These are available at the reference section of AUCA library) Textbooks
Doane, D. & Seward, L. (2013). Applied Statistics in Business and Economics. 4th Ed. New York:
McGraw-Hill Irwin
Groebner, D; Shannon, P. (1985). Business Statistics a Decision-Making Approach. 2nd Ed. United States of
America: Merrill. (519.5 G874).
Healey, J. (2005). Statistics a Tool for Social Research. 7th Ed. United States of America: Thomson. (519.5
H 434)
Hinkle, D., Wiersma, W. & Jurs, S. (2003). Applied Statistics for the Behavioral Sciences. 5th Ed. USA:
University of Toledo.
Howitt, D. & Cramer, D. (2008). Statistics in Psychology. 4th Ed. England: Prentice Hall Europe. (150 H863).
Keller, G. & Warrack, B. (2000). Statistics for Management and Economics. 5th Ed. Canada: Duxbury.
Levine, D. & Stephan, D. (2010). Even You Can Learn Statistics. 2nd Ed. United States of America: Pearson
Education. (519.5 Lev)
Lind, D., Marchal, Wathen, S. (2013). Basic Statistics for Business and Economics, 8th Ed. New York:
McGraw-Hill. (330 LIN. CP.04).
Lind, D., Marchal, Wathen, S. (2008). Statistical Techniques in Business and Economics, 13th Ed. New
York: McGraw-Hill. (519.5/ LIN. CP.02).
Newbold, P; Carlson, W; & Thorne, B. (2010). Statistics for Business and Economics. 7th Ed. United States
of America: Pearson. (330 N533).
Internet Links
Padilla, R. (2011). Course website: Class, data sets, syllabus, handouts, etc. Retrieved from: https://sites.google.com/a/upeu.edu.pe/rosa-padilla/
National Institute of Statistics of Rwanda. Link: https://www.statistics.gov.rw/ National Bank of Rwanda: http://www.bnr.rw/index.php?id=213;
Sooong, T. (2004). Fundamentals of Probability and Statistics for Engineers. Retrieved from: http://international.scholarvox.com/reader/docid/41000606?searchterm=Statistics%20books Deep, R. (2005). Probability and Statistics. Retrieved from:
h t t p : / / i n t e r n a t i o n a l . s c h o l a r v o x . c o m / c a t a l o g / b o o k / d o c i d / 4 1 0 0 1 5 2 1 ? s e a r c h t e r m = S t a t i s t i c s % 2 0 b o o k s
Koenig, D. (2011). Discrete Probability Distribution. Retrieve from: https://www.youtube.com/watch? v=xXW2sy-IOHA&list=PL09A6B27CDCD97205&index=5
Professor Serna. (2011). Introduction to Probability. Retrieved from: https://www.youtube.com/watch?v=-8eSOmTPUbk
Professor Serna. (2011). Conditional Probability. Retrieved from: https://www.youtube.com/watch? v=XYCCWrON7gQ
Koenig, D. (2011). Discrete Probability Distribution. Retrieve from: https://www.youtube.com/watch? v=xXW2sy-IOHA&list=PL09A6B27CDCD97205&index=5
Patrick JMT. (2013). Bayes’ Theorem/Law. Retrieved from: https://www.youtube.com/watch?v=E4rlJ82CUZI Jbstatistics. (2012). An Introduction to Continuous Random Variables. Retrieved from:
https://www.youtube.com/watch?v=OWSOhpS00_s
Dell. (2016). Electronic Textbook by StatSoft - organized by "modules" accessible by buttons, representing classes of analytic techniques. A glossary of statistical terms and a list of references for further study are included. Retrieved from: http://www.statsoft.com/textbook/stathome.html
RStatsInstitute. (2011). Excel and Economics Statistics. Retrieved from: https://www.youtube.com/watch? v=QkG9K7BYz_c&index=1&list=PL09A6B27CDCD97205
Garson, D. (2012). Online Textbook - One of the most comprehensive statistics texts on the internet
presented with a social science orientation. Retrieved from:
Hans Mikelson. (2011). ANOVA Example Part 1 of 2. Retrieved from: http://www.youtube.com/watch? v=ZFCzSRg0ibg&feature=related
15. MODULE TEAM
Dr. Rosa Padilla de Casamayor: Team Leader
…Member
16. Unit approval
Deans and Heads of all Departments contributing to the programme to confirm agreement
FACULTY HOD/DEAN
Education
Signature:
Print Name: Dr. Jacques Kayigema
Dean, Faculty of Education
Signature:
Print Name:
HOD, Department of ELL
Seen and Agreed
Library Signature
Print Name: Mukabariza Rachel (Director)
ICT Signature
Print Name: Dr. Nigigema Papias (Director) Quality office Signature
