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Section outline
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Welcome message
Welcome (Dear Students) to the Module of Introduction to Statistics. It is with pleasure that we would like to welcome you to this module(AST 1231). This module comprises seven units including Introduction, graphical representations, measures of central tendency, measures of Dispersion or Deviations, application of Statistics, regression, and correlations, and Index Numbers.This Module deals with elementary statistical concepts which are used in Applied statistics and Economics. The Module introduces the statistical tools that are useful to analyze univariate, bivariate data, and index numbers. The key objective of this module is to equip learners with essential statistical skills that help to make an effective decision in a real-life situation, especially in business and economics.
Throughout this module, you will find a variety of activities that you are expected to attempt at the end of each section. There will be some questions that will test your level of understanding in each unit. Although answers to these activities are provided at the end of each unit, you can discuss and compare your answers with your colleagues to see how correct or wrong your answers are. You should proceed to the next unit if the activities of the preceding were done without problems.
If you encountered some problems, do more references to the learning materials, go over the content of that particular section in the unit one more, and revise the whole unit. You can also consult your colleagues or subject tutor.Module aim
The module aims at equipping students with comprehensive elementary concepts of statistics that lay a foundation of major areas of Statistics.Indicative contents
This course will cover seven chapters that are divided as follows:- Introduction;
- Charts and graphs;
- Measures of Central Tendency;
- Measures of Dispersion;
- Application of Statistics;
- Regression and Correlation;
- Index numbers.
Learning Outcomes:
By the end of this module you will be able to:- Understand and explain some statistics concepts as tools of analysis of real-life situations, specifically in business;
- Apply the techniques developed in statistics to model and solve real-life problems related to business;
- Explain concepts and basic elements regarding each unit of the entire module;
- Conduct any analysis related to the parameters based on each unit among seven units provide in the module description;
- Apply the necessary technics and methods to improve their performance on gaining knowledge and skills appropriate.
Activities
The activities consist of:- Lectures;
- Group Works / Group Discussions;
- Exercises/Practical;
- Group Assignments;
- Quizzes.
Literature
Read textbooks, published papers, articles, and scientific materials that can be accessed through the UR library website:
https://library.ur.ac.rw/
Assessment strategies,
Continuous courses,
Modules credits: 10
Allocation of study and teaching hours, (see module course)
Total hours: 100Facilitators
The module will be facilitated by :Dr. Daniel Ruturwa , Phone: +250788527050/788305050, E-mail: danielruturwa@gmail.com
Pascal Kayisire, Cell-phone: +250788603244, E-mail: kayisirepascal@gmail.com
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This module has seven learning units:
- Introduction;
- Charts and graphs;
- Measures of Central Tendency;
- Measures of Dispersion;
- Application of Statistics;
- Regression and Correlation;
- Index numbers.
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The storyboard is here attached to show you the module schedule.
Read it please to find the weekly units and units to be covered. Intended learning outcomes, activities where you engage with an outcome where and how the outcome is assessed, and learning resources.21.2 KB -
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You are required to read this important document because it gives more information about the module. The attached document is a PEBL (partnership for enhanced and Blended Learning) of the module of the introduction of Statistics. By reading the PEBL, you will have a common understanding of the aim of the module, get a picture of the brief description of the module, know the intended learning outcomes of modules, indicative content, and the assessment strategies. PEBL indicates all info related to all learning units you will cover, the teaching duration for each unit as well as the knowledge, skills, and attitude you will acquire on completion of this module.
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This chapter introduces the course by defining some concepts and terminologies used in statistics. This chapter intends to give the general overview on tasks dealt with in statistics, types of statistics, types of variables and levels of measurement.
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This introduction chapter describes the preliminary concepts and terminologies used in statistics.
At the end of this chapter you should be able to distinguish:
-The main tasks of statistics, types of statistics, types of variables and levels of measurement.
- sample vs population, census vs sample survey, primary data vs secondary data.
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This activity aims at assessing your understanding on unit I
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This a multiple choice based assessment on section of level of measurement.
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INTRODUCTION
Millions of numerical data are gathered in businesses every day, representing myriad items. For example, numbers represent dollar costs of items produced, geographical locations of retail outlets, weights of shipments, and rankings of subordinates at yearly reviews. No data should be analysed the same way statistically because the entities represented by the numbers are different. For this reason, the business researcher needs to know the level of data measurement represented by the numbers being analysed.
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INTRODUCTION
Statistical data are collected from different sources and different methods are adopted to collect adequate and reliable data. These data are collected to conduct some inquiries or to analyse some problems. Various aspects relating to statistical inquiries and collection of data are the subject matter of this chapter. The business organizations keep the records of their routine transactions, development plans and research reports. Similarly, the Government departments maintain the records regarding the exports, imports, taxes, Government expenditure, births and deaths, price index numbers etc,…Those records are the main sources of data.
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INTRODUCTION
Mean, Median and the Mode are the indices of measures of central tendency.
- The arithmetic mean, the most popular and widely used measure for representing the entire data by one value is what most laymen call an “average” and what the statisticians call the arithmetic mean. Its value is obtained by adding together all the observations and by dividing this total by the number of observations.
- Median is the measure of central tendency, which appears in the “middle” of an ordered sequence of values. That is, half of the observations in a set of data are lower than it and half of the observations are greater than it
- Mode is defined as that value which occurs more time than the others, i.e., having the maximum frequency in the given distribution.
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Aims of the unit
This unit aims to help you to understand the different steps followed on the deviation of statistical parameters like quartiles, quartiles deviations, ranges, variance, and standard deviations with their specific characters and determination.Learning Outcomes:
After successful completion of the unit, you will be expected to be able to:- Explain the concepts regarding this unit,
- Demonstrate the mechanism and the technic that help you to manipulate the necessary formulae, and arrive to execute any possible calculations,
- To do any application required and get the true solutions without difficulty
Indicative content:
- Determination of Range,
- Calculation of quartiles and deduce the quartile deviations,
- Interpretation and roles of quartiles and quartile deviations,
- Variance analysis, its determination, and its statistical role,
- Standard deviation determination and its statistical significance
Reference:
- Read textbooks,
- Published papers, and
- Articles, materials on measures of deviation or dispersion through the University of Rwanda Library website: https:/library.ur.ac.rw/ and materials uploaded below.
Unit outline of this unit:
Attached is the course outline of quartile deviation, variance, and standard deviation, it describes the sub-units covered by the unit and practice to be conducted in the unit.-
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This book contains many chapters, look for chapters related to Unity 4. It can be accessed from https://www.amazon.com/Statistics-Management-Economics-Gerald-Keller/dp/1285425456
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Students mustViewReceive a grade
Quartiles. Quartile deviations and semi-interquartile ranges will be the mains points that you (student) will be focused in this e-tivity; you must be able to
understand the steps to follow and arrive to know well the ways to follow until you find that quartile Q1, Q2 and Q3,and determine their position on the graphs
with their meanings and their interpretations.
Quartiles Deviations:
Similarly, as quartiles are now known, you will follow the steps of deducing the mechanism or technics helping you to determine semi-interquartile range then quartile deviation by applying the appropriate formula studied to determine those parameters,(see, Unit 4.1), in the Lecture notes. This quiz aims to guide you to review how to calculate the quartiles and deduce through the appropriate formulae the quartile deviation. -
Quiz 4.2 : Standard Deviation
At these steps, read more to differentiate the difference between measures of central tendency and measures of dispersion. This reading will enable you to understand well those measures and go deeply for the appropriate comment to each type of measure of deviation. In addition, after reading, through the notes in the above
source related to unit 4.1, you will be guided and able to understand and discuss well this e-tivity and arrive to do it without difficulty. -
E-tivity 4.3: Variance from its components and derivative Forum
This e-tivity will enable you to understand the role of standard deviation in a given distribution.
You have first to review the measures of central tendency and for the measures of dispersions in details. After understanding them well through the sources provided in the note of unit 4, with different components related to the variance, you will easily make a group discuss among the classmates, first to ensure on the components of variance and their different measures. You have also to get a common comprehension even of the used formulae. Also, find out how the task
will be done. After the member groups have the common understand, then each student solves alone this e-tivity, which is presented below: After getting the variance
value, you will deduce its standard deviation or you can proceed by calculation standard deviation and square it. At that steps the obtained value is called ‘’VARIANCE’’.Task: You will follow the steps of getting the standard deviation from the variance.
Given five values of a population: 8, 3, 7,3, and 4.
a. Determine the mean of the population
b. Find the variance of population and the population standard deviation.c. Post your answers in the forum and comment on the answers from your peers.
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After watching this video focusing on measures of dispersion p 20-25, and help to understand the particular important points.
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Aims of the unit:
This unit deals only with statistical practice or how to apply statistics in real-life, like the application of statistics in the business from agriculture, industry, and in any services.Learning Outcomes:
After successful completion of the unit, you will be expected to be able to:- Explain the concepts regarding this unit,
- Demonstrate the mechanism and the technics that help you to manipulate the necessary formulae, and arrive to execute any possible calculations,
- To do any application required and get the true solutions without difficulty
Indicative content:
- Determination of the coefficient of variation of different companies,
- Calculation of mean and standard deviation of different domains,
Reference:
Read textbooks,- Published papers, and
- Articles, materials on the statistical practices in different domains through the University of Rwanda Library website: https:/library.ur.ac.rw/ and materials uploaded below.
Unit outline of this unit:
Attached is the course outline of the coefficient of variation and it describes the sub-units covered by the unit and practice to be conducted in the unit.-
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E-tivity 5.1: Statistical application Forum
A purchasing agent obtained samples of 60-watt bulbs from two companies. He had the samples tested in his own laboratory for the length of life with the following results:
Length of life (in hour) Company A Company B 1 700 and under 1 900
1 900 ” ” 2 100
2 100 ” ” 2 300
2 300 ” ” 2 500
2 500 ” ” 2 70010
16
20
8
63
40
12
3
2(a) Which company’s bulbs do you think are better in terms of an average life?
(b) If prices of both types are the same, which company’s bulbs would you buy and why?Read the note provides by your lecturer regarding coefficient of variation that ensures you to be able to determine the coefficient of variation among the different businesses and arrives to help you to do some appropriate calculation and make a good interpretation, which lead to the good conclusion. In e-tivity 5.1, two companies (industries) produce the bulbs and tubes with different powers. You will be required to read sources careful that help and guide you on how you should proceed to calculate easily the coefficient of variation on any business. Your attention must be focused on how to choose the appropriate company in terms of the average life of bulbs and tubes. In addition, according to the same prix in those companies, provide the true evidences that justify the reasons of choosing X or Y
companies that you want to buy and why? So, your reason can be munched with your evidences and your good appropriate results. -
E-tivity 5.2 : Coefficient of variation Forum
You are given the data pertaining to kilowatt-hours of electricity consumed by 100 persons in NYANZA.
Consumption (K. watt-hours) N° of users 0 but less than 10 6
10 ” ” ” 20 25
20 ” ” ” 30 36
30 ” ” ” 40 20
40 ” ” ” 50 13Calculate: (i). The mean; (Answer: 25.9 K. watt-hours)
(ii). The standard deviation; (Answer: 10.96)
(iii). The range within which the middle 50% of the consumers fall ( Answer: 16.4)
(iv). The coefficient of variation (42.32).Here, you (student) will be sure of the parameters used to determine the coefficient of variation. You will look to obtain the provide answers into e-tivity 5.2, by looking for the ways all answers were obtained. You will also pass through the materials related to the coefficient of the variable. Work in-group discussion which helps to involve more and deeply in statistical technics and to be familiarized with the parameters determining that coefficient of variation that help to get the provided answers through that group discussion.
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Students mustMark as done
The main points here are to know and understand how to know where the prices are stables or not stables even consistency. You will focus more on the note given above in sub-unit five related to the coefficient of variation, which guides you on the choice of the good markets that you can prefer to purchase and get profits. See exercise below:
Month Mumbai Kolkata Month Mumbai Kolkata
January 105 108 June 127 125
February 120 117 July 109 125
March 115 120 August 110 120
April 118 130 September 104 110
May 130 100 October 112 135
Determine the Arithmetic Mean and Standard Deviation of the prices of shares.
In which market are the share prices stable?In this e-tivity, data collection (surveys) will help you to review the precious units (I, II, III & IV), enhancing the skills and the gained knowledge for the previous matters. This will be considered as the key summarizing of unit-5 in statistical applications. The main points here are to know and understand how and where the prices are stables, variabilities, or consistency. You will focus more on the resources provided by your facilitator (Notes) and read other resources obtained through the library, classmates, and other students in the institution. This assignment will help you to contextualize and make a good comparison due to different places of business and arrive to understand how to choose the better one that provides you more benefits.
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Aims of the unit:
This Unit deals only with statistical practice or how to apply statistics in the real life, such that in agriculture, industry, and in any services: banks, tourism, restaurants, hostels, and so on. We are often interested in finding whether a relationship exists between two variables. For example, we would expect there to be a relationship between advertising costs and sales, the more a company spends on advertising, the greater the sales it could expect. To investigate this relationship, we could take a random sample of companies, and ask the companies to state the amount spent on advertising and the corresponding sales of the product.Learning Outcomes:
After successful completion of the unit, you will be expected to be able to:- Explain the concepts regarding this unit,
- Demonstrate the mechanism and the technics that help you to manipulate the necessary formulae, and arrive to execute any possible calculations,
- To do any application required and get the true solutions without difficulty
Indicative content:
- Determination of the coefficient of correlation(Degree of correlation),
- Fit the regression model.
Reference:
- Read textbooks,
- Published papers, and
- Articles, materials on the statistical practices in different domains through the University of Rwanda Library website: https:/library.ur.ac.rw/ and materials uploaded below.
Unit outline of this unit:
Attached is the course outline of the coefficient of variation and it describes the sub-units covered by the unit and practice to be conducted in the unit.-
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E-tivity 6.1: Regression between two variables X and Y Forum
6.1 A: From a set of observations of the variables x and y, it is found that the regression line y on x passes through the point (0; 1.8).
If the means of the x and y values are 5.0 and 8.3 respectively, find the equation of the regression line of y on x in the form: y= a + bx.6.1 B: The table below with two variables X and Y is given.
X 9 8 7 6 5 4 3 2 1 Y 15 16 14 13 11 12 10 8 9 - Find the coefficient of correlation between the variables X, Y, and comment on its value.
- Calculate the regression line of Y on X and X on Y. Give the intersection of two variables
Students have to know well that a regression line is a straight line, which represents the linear relationship between two variables on average. In this step, you have to distinguish their natures (dependent and Independent variables), before their calculation and interpretation of their meanings. You will illustrate this (e-tivity 6.2) with examples in real life.
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Students mustMark as done
A random sample of five (5) college students is selected and their grades in mathematics and statistics are found to be calculated by Spearman’s rank correlation coefficient.
Maths 85 60 73 40 90 Statistics 93 75 65 50 80 Before doing this e-tivity 6.2, read deeply the given materials related to the determination of superman’s rank correlation coefficient through Lecture notes, and other resources given that contribute more to this e-tivity.
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The Goals scored by two teams A and B in a football season were as follows.
Team A 27 9 8 5 4 Team B 17 9 6 5 3 You (student) have to read the materials provide to you in different resources under your position.
In addition, arrive to understand the concept of the simple correlation as the degree of association between two or more variables. For example, the relationships between price and demand, price and supply, age and husband and age of wife, height and weight of individuals, intelligence quotient, and marks secured by students in an examination are some of the examples of a correlation that student must be able to distinguish very well. You have also to distinguish the difference between regression, correlation, and their meaning in life. By reading carefully the materials, you arrive to understand well that correlation is “a statistical tool used to measure the degree of relationship between two or more variables”
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