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Brilliant

Statistics Fundamentals

via Brilliant

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Overview

Statistics starts from data and then asks what was used to generate it. Learning the building blocks — median, mode, range, variance, and standard deviation — will help you analyze graphs, determine statistical significance, and make informed decisions.

By the end of this course, you'll be able to mathematically quantify predictions, use statistical tools to conduct experiments, and discern the truth in a set of data.

Syllabus

  • Statistics Introduction: Learn the tools needed to detect data fakery.
    • Riddles on Averages: Get a feel for statistics by investigating averages.
    • Solving Forward, Solving Backward: How are probability and statistics different?
    • Deception: Explore some cases where statistics can be deceptive.
  • Building Blocks: Everything you need to analyze a set of data.
    • Mean and Median: Learn what mean and median are, how they get applied, and where using them might be inappropriate.
    • Mode: Reckon with the data that appears the most.
    • Quantiles: Split lists in more ways than one.
    • IQR: Consider a metric used to decide outliers.
    • A Probability Refresher: Review some essential probability concepts!
    • Simpson's Paradox: Explore a famous paradoxical situation in which probability seems to defy reality.
  • Lying with Statistics: Use statistics and graphs together to make informed decisions.
    • Scatterplots and Regression: Learn how regressions are made.
    • Regression Paradoxes: Study the drawbacks and confounding aspects of using regressions.
    • Bar and Line Graphs: Check out a wide variety of bar and line graphs that are designed to deceive.
    • More Graphs: What other types of data visualizations are out there, and how might they be used and misused?
    • Cumulative Frequency Plots: Investigate a type of graph that accumulates to 100%.
  • Variance and Normal Curves: Standard deviation, mean, range, and a mathematical mystery...
    • The Two MADs: Learn about two technical statistical metrics.
    • Variance and Standard Deviation: Build and strengthen your intuition for using variance and standard deviation.
    • Building the Normal Curve: Use this puzzle to derive the most famous curve in statistics.
    • Mathematical Bias: When and how can sampling go wrong?
    • The n-1 Mystery: Resolve an algebraic mystery.
  • Experiments: Learn how to manipulate a situation to find a relationship between two variables.
    • Observation vs. Experiment: When can you say a conclusion is sound?
    • Bayesian Probability: Review conditional probability by solving these practice problems.
    • Experiment Design: What's the best way to design an experiment?
    • Blocking: Learn the reasoning behind different methods of sampling.
    • Confidence Intervals: There's always some uncertainty, but just how much?
    • Hypothesis Testing: Get a feel for how margins of error and p-values are really used.
    • Type I and Type II Errors: Account for false positives and false negatives.

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