Introduction to descriptive statistics and central tendency. Ways to measure the average of a set: median, mean, mode.
Course
Statistics
Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!).
62 Lectures
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The difference between the mean of a sample and the mean of a population.
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Variance of a population.
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Using the variance of a sample to estimate the variance of a population.
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Review of what we've learned. Introduction to the standard deviation.
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Playing with the formula for variance of a population.
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Introduction to random variables and probability distribution functions.
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Probability density functions for continuous random variables.
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Basketball binomial distribution.
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Expected value of a random variable.
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Introduction to Poisson Processes and the Poisson Distribution.
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More of the derivation of the Poisson Distribution.
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Introduction to the law of large numbers.
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(Long-26 minutes) Presentation on spreadsheet to show that the normal distribution approximates the binomial distribution for a large number of trials.
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Exploring the normal distribution.
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Discussion of how "normal" a distribution might be.
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Z-score practice.
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Using the empirical rule (or 68-95-99.7 rule) to estimate probabilities for normal distributions.
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Using the Empirical Rule with a standard normal distribution.
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More Empirical Rule and Z-score practice.
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Introduction to the central limit theorem and the sampling distribution of the mean.
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The central limit theorem and the sampling distribution of the sample mean.
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More on the Central Limit Theorem and the Sampling Distribution of the Sample Mean.
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Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean.
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Figuring out the probability of running out of water on a camping trip.
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Estimating the probability that the true population mean lies within a range around a sample mean.
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Mean and Variance of Bernoulli Distribution Example.
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Bernoulli Distribution Mean and Variance Formulas.
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Finding the 95% confidence interval for the proportion of a population voting for a candidate.
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Finding the 95% confidence interval for the proportion of a population voting for a candidate.
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Confidence Interval Example.
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Constructing small sample size confidence intervals using t-distributions.
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One-Tailed and Two-Tailed Tests.
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Z-statistics vs. T-statistics.
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Type 1 Errors.
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Small Sample Hypothesis Test.
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T-Statistic Confidence Interval (for small sample sizes).
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Large Sample Proportion Hypothesis Testing.
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Variance of Differences of Random Variables.
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Difference of Sample Means Distribution.
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Confidence Interval of Difference of Means.
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Clarification of Confidence Interval of Difference of Means.
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Hypothesis Test for Difference of Means.
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Comparing Population Proportions 1.
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Comparing Population Proportions 2.
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Hypothesis Test Comparing Population Proportions.
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Introduction to the idea that one can find a line that minimizes the squared distances to the points.
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Proof (Part 1) Minimizing Squared Error to Regression Line.
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Proof (Part 3) Minimizing Squared Error to Regression Line.
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Proof (Part 4) Minimizing Squared Error to Regression Line.
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Regression Line Example.
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Proof Part 2 Minimizing Squared Error to Line.
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R-Squared or Coefficient of Determination.
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Second Regression Example.
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Calculating R-Squared to see how well a regression line fits data.
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Covariance, Variance and the Slope of the Regression Line.
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Chi-Square Distribution Introduction.
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Pearson's Chi Square Test (Goodness of Fit).
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Contingency Table Chi-Square Test.
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Analysis of Variance 1 - Calculating SST (Total Sum of Squares).
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Analysis of Variance 2 - Calculating SSW and SSB (Total Sum of Squares Within and Between).
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Analysis of Variance 3 -Hypothesis Test with F-Statistic.