Fundamentals of Statistics from edX

Statistics is the science of turning data into insights and ultimately decisions. Behind recent advances in machine learning, data science and artificial intelligence are fundamental statistical principles. The purpose of this class is to develop and understand these core ideas on firm mathematical grounds starting from the construction of estimators and tests, as well as an analysis of their asymptotic performance.

After developing basic tools to handle parametric models, we will explore how to answer more advanced questions, such as the following:

How suitable is a given model for a particular dataset?
How to select variables in linear regression?
How to model nonlinear phenomena?
How to visualize high-dimensional data?

Taking this class will allow you to expand your statistical knowledge to not only include a list of methods, but also the mathematical principles that link them together, equipping you with the tools you need to develop new ones.

This course is part of theMITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.

What's inside

Learning objectives

Construct estimators using method of moments and maximum likelihood, and decide how to choose between them
Quantify uncertainty using confidence intervals and hypothesis testing
Choose between different models using goodness of fit test

Make prediction using linear, nonlinear and generalized linear models
Perform dimension reduction using principal component analysis (pca)

Construct estimators using method of moments and maximum likelihood, and decide how to choose between them
Quantify uncertainty using confidence intervals and hypothesis testing
Choose between different models using goodness of fit test
Make prediction using linear, nonlinear and generalized linear models
Perform dimension reduction using principal component analysis (pca)

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Delves into advanced statistical questions, such as model suitability, variable selection, and nonlinear phenomena

Taught by seasoned instructors with expertise in statistics and machine learning

Provides a solid foundation for data science and machine learning applications

Requires a strong mathematical background, making it suitable for advanced learners

Reviews summary

Challenging but rewarding statistics course

Learners say that this 5-star rated Fundamentals of Statistics course is challenging but rewarding. Reviewers mention that the course covers theoretical and mathematical topics in depth, but this in-depth coverage means that the course is difficult. Reviewers also note that the course is very well organized and that the staff and TAs are supportive.

This course is well organized and the staff is supportive.

"It's very well organized and teached you a lot."

"The course was also perfect."

"Staff team, teach assistants and fellow students was very supportive and always gave some additional clues about existed brainsmashing topics."

This course is challenging, but rewarding.

"It's tough and rigorous."

"This is a tough course, but very rewarding."

"It is one of the hardest classes I've ever taken."

This course covers theoretical and mathematical topics in depth.

"This is a tough course, but very rewarding."

"It covers some of the basics of estimation, such as maximum likelihood, but in a depth which most courses don't take."

"This course is fantastic for a rigorous, theoretical and mathematical tour of statistics."

This course requires a significant time commitment.

"You have to reserve at least 15 h/w"

"If you don't have any backgroud in Stat, you will easily need to spend over 15 hours a week"

"The class material can be divided up to two courses easily to make the material more friendly"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Fundamentals of Statistics with these activities:

Statistics and Probability Review

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Refresh your knowledge of statistics and probability theory, ensuring a solid foundation for the course and improving your ability to grasp advanced concepts.

Browse courses on Statistics

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Review notes from previous coursework or textbooks
Work through practice problems and review online resources
Take a preparatory online course or attend a workshop

Introduction to Statistical Learning

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Build a solid foundation in statistical concepts by delving into this comprehensive textbook, enhancing your understanding of the course material and broadening your knowledge.

View An Introduction to Statistical Learning: with... on Amazon

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Read and summarize key chapters
Attempt practice problems and exercises
Discuss the concepts with classmates or a study group

Statistical Calculations

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Tackle various statistical calculations and problems to solidify your understanding of statistical concepts, building a strong foundation for the course.

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Solve problems from lecture notes and textbook
Attempt practice problems on online platforms
Join or create a study group to discuss problems

Five other activities

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Collaborative Problem-Solving Sessions

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Engage with your peers in collaborative discussions and problem-solving sessions to reinforce your understanding and benefit from diverse perspectives.

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Form study groups or join existing ones
Meet regularly to discuss course material, solve problems, and share insights
Provide constructive feedback to peers and receive feedback on your own work

Machine Learning Case Studies

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Explore real-world applications of machine learning techniques to gain practical insights and better understand their impact on various industries.

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Identify a specific machine learning case study and research its implementation
Review research papers and articles related to the case study
Present your findings to your peers or in an online forum

Data Visualization Project

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Showcase your ability to present data insights effectively by creating interactive data visualizations that communicate complex information in a clear and engaging manner.

Browse courses on Data Visualization

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Choose a dataset and identify the key insights you want to convey
Experiment with different visualization techniques
Create interactive dashboards or visualizations using tools like Tableau or Power BI
Present your visualizations and discuss their impact and limitations

Become a Peer Mentor

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Deepen your understanding of the course material by sharing your knowledge and providing support to fellow students, solidifying your grasp of concepts and enhancing your communication skills.

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Identify opportunities to mentor other students
Join or create mentorship programs
Provide guidance, answer questions, and offer encouragement to peers

Statistical Simulation Project

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Develop your understanding of statistical inference and probability theory by designing and implementing statistical simulations to solve complex problems.

Browse courses on Monte Carlo Methods

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Define the research question and the variables involved
Build a simulation model using tools like R or Python
Collect and analyze the simulation results
Write a report summarizing the findings and limitations

Career center

Learners who complete Fundamentals of Statistics will develop knowledge and skills that may be useful to these careers:

Data Scientist

A Data Scientist designs, collects, analyzes, and interprets data to find trends and insights that inform decision-making. Knowledge of hypothesis testing and statistical principles from the course "Fundamentals of Statistics" is essential, as they provide the foundation for understanding how to collect, analyze, and interpret data accurately. By taking this course, you'll gain a deep mastery of the mathematical grounds of statistics, enabling you to better design and execute data-driven solutions as a Data Scientist.

See salaries and explore the career path for Data Scientist

Statistician

A Statistician applies statistical theory and methods to a wide range of fields, such as medicine, public health, and finance. The course "Fundamentals of Statistics" covers the core ideas of statistics, including how to construct estimators, perform hypothesis testing, and analyze the asymptotic performance of statistical models. By gaining a strong foundation in these principles, you'll be well-equipped to develop and apply statistical methods for solving real-world problems as a Statistician.

See salaries and explore the career path for Statistician

Quantitative Analyst

A Quantitative Analyst (Quant) uses mathematical and statistical models to analyze financial data and make investment decisions. The course "Fundamentals of Statistics" provides a strong foundation in statistical principles, including hypothesis testing and model selection, which are essential for developing and evaluating financial models. By taking this course, you'll gain the quantitative skills necessary to succeed in a career as a Quant.

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Machine Learning Engineer

A Machine Learning Engineer designs, develops, and maintains machine learning models to solve business problems. The course "Fundamentals of Statistics" covers the foundations of statistical modeling, including how to choose between different models, make predictions, and perform dimension reduction. This knowledge is crucial for understanding the principles underlying machine learning algorithms and developing effective ML solutions.

See salaries and explore the career path for Machine Learning Engineer

Data Analyst

A Data Analyst collects, processes, and analyzes data to extract insights and inform decision-making. The course "Fundamentals of Statistics" provides a strong foundation in statistical principles and methods, including data visualization, hypothesis testing, and model selection. By developing these skills, you'll be well-prepared to perform data analysis and communicate insights effectively as a Data Analyst.

See salaries and explore the career path for Data Analyst

Financial Analyst

A Financial Analyst uses financial data and statistical models to evaluate investment opportunities and make recommendations. The course "Fundamentals of Statistics" covers the basics of statistical modeling, including how to construct estimators, perform hypothesis testing, and select between different models. By gaining this knowledge, you'll be able to analyze financial data, develop investment strategies, and provide informed advice as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Business Analyst

A Business Analyst uses data analysis and statistical methods to solve business problems and improve organizational performance. The course "Fundamentals of Statistics" provides a foundation in statistical principles and techniques, including data visualization, hypothesis testing, and model selection. With this knowledge, you'll be able to leverage data to identify opportunities, develop solutions, and make better decisions as a Business Analyst.

See salaries and explore the career path for Business Analyst

Market Researcher

A Market Researcher conducts research to understand consumer behavior and market trends. The course "Fundamentals of Statistics" provides a strong foundation in statistical methods and data analysis techniques. By taking this course, you'll gain the skills necessary to design and execute market research studies, analyze data, and draw meaningful conclusions, which will help you succeed as a Market Researcher.

See salaries and explore the career path for Market Researcher

Data Engineer

A Data Engineer designs, builds, and maintains data infrastructure and systems to support data analysis and machine learning. The course "Fundamentals of Statistics" provides a foundation in statistical principles and data analysis techniques. By taking this course, you'll gain the knowledge necessary to understand the data landscape, design efficient data pipelines, and collaborate effectively with data scientists and other stakeholders as a Data Engineer.

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Software Engineer

A Software Engineer designs, develops, and maintains software applications. While not directly related to statistics, the course "Fundamentals of Statistics" can provide a valuable foundation for Software Engineers who work on data-driven applications or who need to understand statistical concepts to develop more robust and efficient software solutions.

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Product Manager

A Product Manager manages the development and launch of new products or features. The course "Fundamentals of Statistics" can provide a valuable foundation for Product Managers who need to understand statistical concepts to make informed decisions about product design, pricing, and marketing.

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Operations Research Analyst

An Operations Research Analyst uses mathematical and statistical models to solve complex business problems. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to develop and analyze models to optimize processes, improve efficiency, and make better decisions as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Risk Analyst

A Risk Analyst identifies, assesses, and manages risks to an organization. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to analyze data, develop risk models, and make informed decisions to mitigate risks effectively as a Risk Analyst.

See salaries and explore the career path for Risk Analyst

Actuary

An Actuary uses mathematical and statistical models to assess and manage financial risks. The course "Fundamentals of Statistics" provides a foundation in statistical principles and modeling techniques. By taking this course, you'll gain the skills necessary to develop and analyze models to evaluate insurance risks, set premiums, and make informed decisions as an Actuary.

See salaries and explore the career path for Actuary

Epidemiologist

An Epidemiologist investigates the causes and patterns of diseases in populations. The course "Fundamentals of Statistics" provides a foundation in statistical principles and data analysis techniques. By taking this course, you'll gain the skills necessary to design and conduct epidemiological studies, analyze data, and draw meaningful conclusions to inform public health policy and practice as an Epidemiologist.

See salaries and explore the career path for Epidemiologist