Online Class: Statistics 101
This statistics course introduces the basic concepts of statistical analysis, with a focus on both univariate (single-variable) and bivariate (two-variable) data. The course starts with an introduction to statistics terms and then moves on to organization and display of data. Analysis of univariate data by way of measures of central tendency (such as the mean or average), dispersion (such as the variance), and asymmetry ("skewness") is presented next, followed by an introduction to probability theory.
The relationship of probability to statistics is also discussed, providing students with the tools they need to understand how "chance" plays a role in statistical analysis. Statistical distributions, with a focus on the normal distribution and its uses, are also considered, along with a discussion of bivariate data and linear (least-squares) regression. Finally, the course culminates with a low-level introduction to hypothesis testing. Although this last topic could be a course of its own, the student is provided with enough theory and sufficient practice to conduct analyses of simple statistical hypotheses.
Statistics is a subject that has earned a certain amount of notoriety because of its misuse in various contexts. Nevertheless, statistics is a tool that, if used properly, can be of tremendous help in math, science, engineering, history, politics, and numerous other fields. As you study this subject, always keep in mind that statistics is more than just math: it is not simply manipulation of numbers through addition, subtraction, multiplication, division, and other mathematical operations. Statistics also involves language and units: when a statistician (or layman) provides a statistic, it involves a number and a label of some sort. For instance, the number 5.3 is not in and of itself a statistical value; "an average age of 5.3 years," however, is a statistical value. This linguistic aspect of statistics sometimes allows a certain amount of ambiguity that can be misleading. By studying statistics, you will equip yourself to identify and understand both uses and abuses of this tool.
What is Statistics?
Statistics is used for quantifying sets of data such as attributes of a group of people and measurements taken in a laboratory. Consider, for instance, the population of a particular country. The people who reside in that country have varying heights: some are short, some are tall, some are in between. If we wanted to compare the height of this population with that of some other population in a convenient manner, we would not want to compare individual people. Such a task would be burdensome (the number of people in a country might be in the millions or billions) and would not necessarily be particularly helpful as a means of comparing populations as a whole. Instead, we can use an average or median height as the basis for our comparison. These statistical values are single numbers that quantify the data (the heights of a country's population) and that provide a convenient way to express and compare certain characteristics of those data. Part of the goal of this course is to teach you how to select and use statistical tools like averages and medians, as well as a host of others, in assessing and comparing data.
Simply defined, statistics (sometimes colloquially termed "stats") is the study of collecting, analyzing, interpreting, and representing of sets of numerical data. Thus, virtually any field of study that uses numbers can, at least occasionally, involve statistics. Statistics, because it makes extensive use of numbers, is math-intensive, and a decent grasp of basic arithmetic and algebra is required to study this field.
Lesson 1 - Statistics Terms and MotivationThis lesson will explain why the study of statistics is important, and it will introduce you to some of the key terms and ideas that will be critical to understanding subsequent lessons.
Lesson 2 - Displaying Statistical DataThis lesson will teach you to recognize and construct tabular and graphical representations of data, which is a crucial skill that you will use in later chapters.
Lesson 3 - Measures of Central TendencyIn this lesson, you will learn how to describe the "central tendency" of a data set--that is, a number that characterizes the "center" of the data.
Lesson 4 - Selecting an Appropriate Measure of Central TendencyNow that we have studied several different measures of central tendency, we now consider some of the factors that you must take into account when selecting an appropriate measure of central tendency
Lesson 5 - Measures of DispersionThis lesson introduces you to measures of dispersion, which quantify how widely data is spread around the mean.
Lesson 6 - Measures of AsymmetryIn this lesson, we will study a measure of asymmetry--skewness--which quantifies how data is "skewed" to either side of the mean.
Lesson 7 - Other Statistical MeasuresThis lesson introduces several more miscellaneous statistical measures that can be useful in certain contexts.
Lesson 8 - Introduction to Probability IAlthough probability theory could constitute a course of its own, a brief presentation of some of the elements of this area is helpful for our study of statistics.
Lesson 9 - Introduction to Probability IIThis lesson discusses how we can solve probability problems by counting the number outcomes of a particular random experiment.
Lesson 10 - Statistical DistributionsThis lesson combines what we've learned in both statistics and probability and applies this knowledge to statistical (probability) distributions.
Lesson 11 - The Normal DistributionThis lesson presents the normal distribution, which is a widely used statistical distribution, as well as how to use it to calculate probabilities.
Lesson 12 - Bivariate DataThis lesson introduces bivariate data distributions and discusses some related concepts such as scatterplots, marginal distributions, and independence of random variables.
Lesson 13 - Regression AnalysisThis lesson introduces the concept of regression with a focus exclusively on least-squares linear regression.
Lesson 14 - Introduction to Hypothesis Testing IThis lesson brings together much of what we have learned so far and applies it to statistical hypothesis testing.
Lesson 15 - Introduction to Hypothesis Testing IIThe final lesson in this course provides a brief overview of the types of errors associated with hypothesis testing and also provides practice problems to reinforce the concepts and skills studied throughout this course.
- Define statistics terms.
- Display statistical data.
- Define measures of central tendency.
- Select an appropriate measure of central tendency.
- Define measures of dispersion.
- Describe measures of asymmetry.
- Describe Probability I problems
- Describe and solve Probability II problems.
- Summarize statistical distributions.
- Describe the normal distribution.
- Describe bivariate data.
- Perform regression analysis.
- Describe Hypothesis Testing I and II.
- Demonstrate mastery of lesson content at levels of 70% or higher.
Additional Course Information
- Document Your Lifelong Learning Achievements
- Earn an Official Certificate Documenting Course Hours and CEUs
- Verify Your Certificate with a Unique Serial Number Online
- View and Share Your Certificate Online or Download/Print as PDF
- Display Your Certificate on Your Resume and Promote Your Achievements Using Social Media
- "Great timely feedback!" -- Audrey K.
- "I found that the course resources helpful. I needed it especially for the lesson on normal distriuubtion. I needed to refer to it for the z-scores." -- Tiffany L.
- "I found the course very interesting and the instructor was very helpful. Well organized chapters and the practice problems." -- Gayatri M.
- "I found all the parts to be helpful." -- Nancy G.
- "My course instructor was very prompt in providing feedback and responding to emails and tried to clarify concepts that I had questions on." -- Kimberlly S.
- "I like that the course was organized well." -- Kimberlly S.
- "Very knowledgeable and helpful instructor. This course set-up is much more user friendly than other statistics refreshers I have tried." -- Julie R.
- "The lessons are laid out very nicely. They tell you what you need to now for the most part. My instructor answered questions promptly and with detail." -- Julie R.
- "The instructor is wonderful. I would have him as an instructor again." -- Cynthia M.
- "The Instructor was very pleasant, offering words of encouragement when I did poorly on the second exam. He was fairly prompt with grading assignments and answering emails. I would recommend him for this class in the future." -- Jessica S.
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