MATH 1280 — Introduction to Statistics
My personal experience and tips for this course
👋 Welcome to MATH 1280
Hi, if you are planning to take “Introduction to Statistics” at University of the People (UoPeople), then this article is for you. I took this course from February to April 2020 and let me tell you that this has been one of the most amazing learning experiences for me. The course truly showed me how powerful statistics can be to analyze real-world scenarios.
One of the most amazing things about this course is that it teaches statistics using R, a programming language specifically used for statistical analysis. This made the experience much more interactive, enjoyable, and realistic. Learning the basics of R is an added value of this course, a new skill that you can use in your daily work and include in your CV. ✨
The quality of the assignments and assessments in this course was extraordinary. Each assignment, self-quiz, and graded quiz is carefully designed with questions that will accurately test your understanding and help you determine which topics you need to review each week.
💡 Tip: Just like College Algebra, this course is required to start taking more advanced Computer Science courses.
As you can see, this course (like all courses) will require time and effort, so…
Be prepared to work hard from day one.
Do not underestimate the amount of time that you will need to dedicate to this course. Solving exercises and practicing your R skills require time, in addition to the time required to complete the assignments, study, and assess your peers’ work. So be prepared to allocate the necessary time per week. Plan ahead because assignments can be very detailed and challenging.
As a reference, this course took me approximately 19–24+ hours per week.
Now let’s see what you will learn during the course.
📚 Course Content
Let me start by giving you a brief overview of the topics covered per week (one unit per week):
- Unit 1: Introduction
During this unit, you will learn fundamental concepts such as population, sample, sampling, variable, statistic, parameter, data, and the basics of the R programming language. This week will not require as much time as other weeks, but it’s a great opportunity to dive deeper into basic aspects of statistics.
💡 Tip: During this first unit, my top tip would be to focus on familiarizing yourself with the R programming language. I personally researched more about the language, about the R console and, if you are working with R studio, more about this IDE. I also recommend researching more about the difference between a statistic and parameter. This will be key for the coming weeks.
- Unit 2: Sampling and Data Structures
During this unit, you will learn key concepts like frequency, relative frequency, and cumulative frequency. This week is really awesome because you will start solving exercises and completing frequency tables. You will also learn how to critically assess the process of sampling (selecting a sample from a population). You will learn how to read data from a CSV file in R and the types of data that you can work with.
💡 Tip: As the course progresses, each week will require more effort and time and the topics will become more challenging, so do not underestimate the workload during the course.
- Unit 3: Descriptive Statistics
During this unit, you will dive into a critical aspect of descriptive statistics: presenting data using plots and graphs. Particularly, you will learn how to make and interpret bar plots, histograms, and box plots. You will learn concepts like the mean, median, quartiles, skewness, and outliers. You will also learn how to identify outliers. In addition, you will learn how to calculate statistics that help you determine the spread of the data such as the variance and the standard deviation.
💡 Tip: As you can see, this week will require more time because the concepts presented are key to succeed in this course. Trust me, you will need to understand these concepts completely before moving on because you will use them constantly.
- Unit 4: Probability
This unit presents a topic that at first might seem a little bit more abstract or theoretical: probability. During this week you will learn concepts like random variable, sample space, distribution of a random variable, event, and expectation and variance of a random variable. You will learn how to identify and calculate them using specific formulas that, if you practice enough, you will learn by heart in the coming weeks. I seriously suggest making a summary of the formulas presented during this week.
💡 Tip: If you are completely new to probability theory, then this week will probably be one of the most challenging weeks for you. I’m telling you this because it is very important to take this week very seriously and dedicate enough time and effort to truly understand these concepts. This unit will give you the foundation that you need to succeed in weeks 5–8, so it’s extremely important.
- Unit 5: Random Variable
During this unit, you will learn more about random variables. This unit is essentially based on your previous knowledge of probability (see why Unit 4 is so important?). You will learn that there are two types of random variables: discrete and continuous. You will learn how to work with Binomial Random Variables, Poisson Random Variables, Uniform Random Variables, and Exponential Random Variables. You will also learn how to interpret the graphs of probability density functions.
This unit is amazing! 🎉 I think this was my favorite unit of the entire course because I learned how to identify the type of random variable that I had to work with based on the characteristics of the scenario that I was trying to model.
You will use R to visualize the distributions and how they vary depending on the values of their parameters. My suggestion would be to experiment with these values until you truly understand how they affect the shape of the distribution (this is what made these concepts “click” for me during this week).
💡 Tip: Each distribution has particular characteristics, parameters, and formulas that you will need to use to find the expectation, variance, probability, and cumulative probability, so making a summary of these characteristics and formulas is vital to have a quick reference as you work on your assignments.
- Unit 6: The Normal Random Variable
After Unit 5, you will know how to work with four probability distributions, but there is another probability distribution that is very important for statistics, perhaps the most important distribution of all: the Normal distribution (you can see a graph of this distribution below, a graph that I generated using R). During this week, you will learn how to work with this distribution and how to generate what is called the Standard Normal Distribution with z-scores. You will also learn how to compute percentiles using the Normal distribution, how to find possible outliers in this distribution, and how to approximate it using other distributions with and without continuity corrections.
💡 Tip: This probability distribution is super important for statistics. After this unit, you will be able to work with it and interpret it to analyze real-world scenarios. Awesome, right? 👍 Working with R will make the process much more interactive, so be sure to experiment with the parameters and generate many graphs in R to visualize the changes.
- Unit 7: Sampling Distribution
During this week, you will learn about the sampling distribution. An awesome fact is that when you take many repeated samples, the distribution of the mean resembles a Normal distribution, regardless of the distribution of the original data. This is stated by the Central Limit Theorem. You will confirm this by running simulations in R and plotting your results. At this point in the course, you will find this fascinating (I know did! 😊) During this week, you will also learn about the Law of Large Numbers.
💡 Tip: Make sure that you understand well-enough how the simulations work. Adapt them to new scenarios and test your understanding. You will review these topics again in Unit 8, but understanding them as soon as possible is key to succeed in the assignments and final exam.
- Unit 8: Overview and Integration
This is the last week of the course. During this week, you will practice with solved exercises from the main textbook that combine all the concepts that you learned in the course. These problems will take your knowledge to a whole new level. It’s really awesome. By this point, you will feel that your skills have improved tremendously and that now you are capable of analyzing more complex real-world scenarios.
💡 Tip: During this unit, I really suggest researching more about the Central Limit Theorem for Sums. I found this very helpful.
After this unit, you will take the final exam.
✍️ Study Tips and Helpful Resources
Use the Feynman technique
This study technique is completely awesome. It basically consists of taking a blank sheet of paper and using it as if you were teaching a class in a whiteboard. Explain the concepts as if you were teaching them to someone who is completely new to the subject and try to make them as simple as possible.
Include examples, make diagrams, add analogies to illustrate what is happening behind the scenes, review formulas and explain each part of each formula using your own words.
It’s your class and your goal is to explain it in the best possible way.
If you realize that you are not as clear as you should be on certain aspects of the topic that you are trying to explain, review them using your notebook or textbook and break them down to the point where you do understand what is happening behind the scenes.
I used this technique during the course and it truly helped me understand and remember the content better. It’s so practical and engaging that I promise you that your study session will be awesome! 👍
This is a great article about the Feynman Technique.
Take detailed notes
You will notice that the readings for this course are relatively shorter than the readings that you will find in other courses, but they do require approximately the same amount of time because you will need to analyze and internalize the content and examples.
Your notes will be amazing tools to help you understand and review the content. I personally like to take handwritten notes, but you can also use your computer to take digital notes. Just make sure that you develop a technique that works for you and summarize the content as much as possible, keeping only the essential aspects of each topic.
Run the R Commands Yourself and Experiment With The Code
In the main textbook, you will find many R commands that are used to explain concepts and perform simulations. Understanding how this code works is key because you will need to use your own code to answer questions during the assessments. Analyze how each line works and what each command does.
My suggestion would be to write down the commands in your notebook with a brief description of what they do, what parameters they take, and how those parameters affect the result.
💡 Tip: You can browse the documentation using ?<function>
Make Weekly Summaries and Study Guides
I personally find this very helpful. Writing down the content in your words will help you remember.
Review the Solved Exercises from the Textbook
At the end of each chapter of the main textbook (a textbook written specifically for the course), you will find a few solved exercises. They are priceless to help you understand how to apply the concepts that you learned during the unit.
Go over them in detail and try to solve them first without looking at the solution. Then, if you made a mistake, reflect on why you made the mistake and write the explanation down in your notebook.
Use all the Additional Resources Provided
The course includes material specially made for UoPeople such as a textbook, an annotated version of the textbook, a PDF file with helpful tips for each unit, and a PDF summary of the characteristics of the probability distributions.
Use them all. Read them all, even if some of them are optional.
This is one of the most important tips that I can give you in this article.
Read the OpenStax book “Introductory Statistics”
During the course, I really liked to complement my learning with this book. It’s free and you can download it as a PDF file. I feel that its exercises and examples can be a great addition to your learning experience. I really liked this book and I’m super thankful to this organization for providing free access to these amazing college books.❤️
You can download the book here, in the OpenStax website.
💡 Tip: The book covers various topics, so you will need to find the sections that are relevant to you.
Watch Khan Academy’s Video Lectures
If you like watching video lectures, this Khan Academy course “Introduction to Statistics” might be helpful for you.
Start your Assignments Early
This is my final tip for you: start your assignments early in the learning week.
You will need to submit your assignments by Wednesday (only one of them can be submitted on Thursdays, Learning Journals).
Your Discussion Assignment should be submitted as early as possible to start discussing the topic with your peers. I personally like to post my discussion assignments on Mondays, so I start reading the topic on Thursdays.
Time is your most precious tool as an online student, use it well and you will succeed.
✨ Good Luck!
I wish you much success during this course and during your UoPeople journey! Your claps 👏 are much appreciated.
I really hope you liked my article. Follow my Medium Publication My UoPeople CS Journey to read about my experience during the degree 🎓.
