Course

# Statistics

Introduction to statistics. Will eventually cover all of the major topics in a first-year statistics course (not there yet!).

## 62 Lectures

• ### Statistics: The Average

00:12:35

Introduction to descriptive statistics and central tendency. Ways to measure the average of a set: median, mean, mode.

• ### Sample vs. Population Mean

00:06:42

The difference between the mean of a sample and the mean of a population.

• ### Variance of a Population

00:12:23

Variance of a population.

• ### Sample Variance

00:11:18

Using the variance of a sample to estimate the variance of a population.

• ### Standard Deviation

00:13:07

Review of what we've learned. Introduction to the standard deviation.

• ### Alternate Variance Formulas

00:12:17

Playing with the formula for variance of a population.

• ### Introduction to Random Variables

00:12:04

Introduction to random variables and probability distribution functions.

• ### Probability Density Functions

00:10:02

Probability density functions for continuous random variables.

00:13:26

• ### Expected Value: E(X)

00:14:53

Expected value of a random variable.

• ### Poisson Process 1

00:11:01

Introduction to Poisson Processes and the Poisson Distribution.

• ### Poisson Process 2

00:12:41

More of the derivation of the Poisson Distribution.

• ### Law of Large Numbers

00:08:59

Introduction to the law of large numbers.

• ### Normal Distribution Excel Exercise

00:26:04

(Long-26 minutes) Presentation on spreadsheet to show that the normal distribution approximates the binomial distribution for a large number of trials.

• ### Introduction to the Normal Distribution

00:26:24

Exploring the normal distribution.

• ### Qualitative Sense of Normal Distributions

00:10:53

Discussion of how "normal" a distribution might be.

• ### Emperical Rule

00:10:25

Using the empirical rule (or 68-95-99.7 rule) to estimate probabilities for normal distributions.

• ### Standard Normal Distribution and the Empirical Rule

00:08:16

Using the Empirical Rule with a standard normal distribution.

• ### More Emperical Rule and Z-Score Practice

00:05:57

More Empirical Rule and Z-score practice.

• ### Central Limit Theorem

00:09:49

Introduction to the central limit theorem and the sampling distribution of the mean.

• ### Sampling Distribution of the Sample Mean Part 1

00:10:52

The central limit theorem and the sampling distribution of the sample mean.

• ### Sampling Distribution of the Sample Mean Part 2

00:13:20

More on the Central Limit Theorem and the Sampling Distribution of the Sample Mean.

• ### Standard Error of the Mean

00:15:15

Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean.

• ### Sampling Distribution of the Sample Mean

00:14:28

Figuring out the probability of running out of water on a camping trip.

• ### Confidence Interval 1

00:14:03

Estimating the probability that the true population mean lies within a range around a sample mean.

• ### Mean and Variance of Bernoulli Distribution Example

00:08:20

Mean and Variance of Bernoulli Distribution Example.

• ### Bernoulli Distribution Mean and Variance Formulas

00:06:59

Bernoulli Distribution Mean and Variance Formulas.

• ### Margin of Error 1

00:15:02

Finding the 95% confidence interval for the proportion of a population voting for a candidate.

• ### Margin of Error 2

00:10:05

Finding the 95% confidence interval for the proportion of a population voting for a candidate.

• ### Confidence Interval Example

00:18:36

Confidence Interval Example.

• ### Small Sample Size Confidence Intervals

00:11:11

Constructing small sample size confidence intervals using t-distributions.

• ### One-Tailed and Two-Tailed Tests

00:11:26

One-Tailed and Two-Tailed Tests.

• ### Z-statistics vs. T-statistics

00:06:34

Z-statistics vs. T-statistics.

• ### Small Sample Hypothesis Test

00:09:04

Small Sample Hypothesis Test.

• ### T-Statistic Confidence Interval

00:11:47

T-Statistic Confidence Interval (for small sample sizes).

• ### Large Sample Proportion Hypothesis Testing

00:14:30

Large Sample Proportion Hypothesis Testing.

• ### Variance of Differences of Random Variables

00:10:47

Variance of Differences of Random Variables.

• ### Difference of Sample Means Distribution

00:12:18

Difference of Sample Means Distribution.

• ### Confidence Interval of Difference of Means

00:15:49

Confidence Interval of Difference of Means.

• ### Clarification of Confidence Interval of Difference of Means

00:02:41

Clarification of Confidence Interval of Difference of Means.

• ### Hypothesis Test for Difference of Means

00:10:06

Hypothesis Test for Difference of Means.

• ### Comparing Population Part 1

00:10:47

Comparing Population Proportions 1.

• ### Comparing Population Part 2

00:10:00

Comparing Population Proportions 2.

• ### Hypothesis Test Comparing Population Proportions

00:16:13

Hypothesis Test Comparing Population Proportions.

• ### Squared Error of Regression Line

00:06:47

Introduction to the idea that one can find a line that minimizes the squared distances to the points.

• ### Minimizing Squared Error to Regression Line Part 1

00:10:35

Proof (Part 1) Minimizing Squared Error to Regression Line.

• ### Minimizing Squared Error to Regression Line Part 3

00:10:54

Proof (Part 3) Minimizing Squared Error to Regression Line.

• ### Minimizing Squared Error to Regression Line Part 4

00:04:18

Proof (Part 4) Minimizing Squared Error to Regression Line.

• ### Regression Line Example

00:09:27

Regression Line Example.

• ### Minimizing Squared Error to Regression Line 2

00:09:54

Proof Part 2 Minimizing Squared Error to Line.

• ### R-Squared or Coefficient of Determination

00:12:41

R-Squared or Coefficient of Determination.

• ### Second Regression Example

00:09:15

Second Regression Example.

• ### Calculating R-Squared

00:09:45

Calculating R-Squared to see how well a regression line fits data.

• ### Covariance and the Regression Line

00:15:08

Covariance, Variance and the Slope of the Regression Line.

• ### Chi-Square Distribution Introduction

00:10:23

Chi-Square Distribution Introduction.

• ### Pearson's Chi Square Test (Goodness of Fit)

00:11:48

Pearson's Chi Square Test (Goodness of Fit).

• ### Contingency Table Chi-Square Test

00:17:37

Contingency Table Chi-Square Test.

• ### Calculating SST (Total Sum of Squares)

00:07:39

Analysis of Variance 1 - Calculating SST (Total Sum of Squares).

00:13:20