Mathematics
MTH1495 ccs
Introduction to Statistics

This course from Saylor.org introduces the fundamental concepts of statistics. The course description provided by Saylor.org is as followed: In this course, you will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. You will learn about how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. Statistics formalizes the process of making decisions, and this course is designed to help you use statistical literacy to make better decisions.

6 Units

### Unit 1: Data and Descript...

Unit description from Saylor.org: In today's world we access and use large volumes of data every day. The first step of data analysis is to accurately summarize this data, both graphically and numerically, so that we can understand what the data is saying. To be able to use and interpret data correctly is essential to making informed decisions. In this unit you will learn about descriptive statistics, which is used to summarize and display data. After completing this unit, you will know what you can do to present data that you have collected.

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Reading pie graphs (circle graphs)

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Stem-and-Leaf Plots

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Statistics: The Average

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Statistics: Sample vs. Population Mean

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Statistics: Variance of a Population

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Statistics: Sample Variance

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Statistics: Standard Deviation

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Statistics: Alternate Variance Formulas

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Lecture 1: Sampling and Data

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Lecture 2: Descriptive Statistics

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Sampling and Data Practice

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Center of the Data Practice

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Spread of the Data Practice

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Chapter 1: Sampling and Data

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Chapter 2: Descriptive Statistics

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1.2 Descriptive Statistics: Displaying Data

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1.3 Descriptive Statistics: Measure

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Mean, median, & mode example

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Constructing a box plot

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Range and Mid-Range

### Unit 2: Probability Topic...

Unit Description from Saylor.org: After you have learned to describe and display data, how can you use the sample data to draw conclusions about the populations? To answer this question, you need probability, a subject we will explore over the course of this unit.

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Lecture on Topics in Probability

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Unit 2 Outline

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Calculating Probabilities Practice

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Probability Contingency Tables Practice

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Chapter 3: Probability Topics

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2.1 Probability Overview

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2.2 Independent and Mutually Exclusive Events

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2.3 Two Basic Rules of Probability

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2.4 Contingency Tables, Venn Diagrams, and Tree Di...

### Unit 3: Random Variables ...

Description from Saylor.org: In the last unit, you learned how to calculate probabilities in the framework of sample spaces, outcomes, and events. In this unit, you will build on those ideas and learn about random variables. A random variable describes the outcomes of a statistical experiment. A statistical distribution describes the numbers of times each possible outcome occurs in a sample. The values of a random variable can vary with each repetition of an experiment. Intuitively, a random variable is an observable that takes on values with certain probabilities.

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Introduction to Random Variables - Khan

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Probability Density Functions - Khan

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Binomial Distribution I

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Standard Normal Distribution and the Empirical Rul...

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Binomial Distribution II

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Binomial Distribution III

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Binomial Distribution IV

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Expected Value of Binomial Distribution

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Poisson Process 1

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Poisson Process II

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Law Of Large Numbers

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Normal Distribution Excel Exercise

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Introduction to the Normal Distribution

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Qualitative Sense of Normal Distribution

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Normal Distribution Problems: z-score

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Normal Distribution Problems: Empirical Rule

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Lecture 4: Discrete Distributions

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Lecture 5: Continuous Random Variables

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Lecture 6: The Normal Distribution

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Unit 3 Outline

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Uniform Distribution Practice

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Binomial Distribution Practice

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Exponential Distribution Practice

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Poisson Distribution Practice

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Geometric Distribution

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Hypergeometric Distribution

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The Normal Distribution Practice

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Discrete Distributions Practice

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Chapter 4: Discrete Random Variables

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Chapter 5: Continuous Random Variables

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Chapter 6: The Normal Distribution

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3.1 Discrete Random Variables and Discrete Probabi...

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3.2 Continuous Random Variables

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3.3 Normal Distribution

### Unit 4: Central Limit The...

The unit description from Saylor.org: In this unit, you will learn how to use the central limit theorem and confidence intervals, the latter of which enable us to estimate unknown population parameters. The central limit theorem provides us a way to make inference from samples of non-normal populations. This theorem states that given any population (regardless of whether or not it is a normal distribution), as the sample size increases, the sampling distribution of the means approaches a normal distribution. It is a powerful theorem because it allows us to assume that given a large enough sample, the sampling distribution will be normally distributed. The central limit theorem is one of the most important ideas in statistics, so be sure to spend time on it.

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Central Limit Theorem

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Sampling Distribution of the Sample Mean

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Sampling distribution of the sample mean 2

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Sampling Distribution Example Problem

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Confidence Interval 1

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Margin of Error I

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Margin of Error II

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Confidence Interval Example

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Small Sample Size Confidence Intervals

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Small Sample Hypothesis Test

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Lecture 7: The Central Limit Theorem

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Lecture 8: Confidence Intervals

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Unit 4 Outline

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The Cental Limit Theorem Practice

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Confidence Intervals for Averages Practice 1

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Confidence Intervals for Averages Practice 2

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Confidence Intervals for Proportions Practice

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Chapter 7: The Central Limit Theorem

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Chapter 8: Confidence Intervals

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4.1 The Central Limit Theorem

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4.2 Confidence Intervals

### Unit 5: Hypothesis Testin...

The unit description from Saylor.org: One of the major goals in statistics is to use the information you collect from a sample to get a better idea of the entire population in which you are interested. In this unit, you will learn about hypothesis testing, which will enable you to achieve that goal. A hypothesis test involves collecting and evaluating data from a sample to make a decision as to whether or not that data supports a claim made about a population. This unit will also teach you how to conduct hypothesis tests and to identify and differentiate between the errors associated with them.

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Type 1 Errors

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Large Sample Proportion Hypothesis Testing

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Difference of Sample Means Distribution

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Confidence Interval of Difference of Mean

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Hypothesis Test for Difference of Means

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Comparing Population Proportions I

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Comparing Population Proportions II

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Hypothesis Test Comparing Population Proportions

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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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Lecture 9: Hypothesis Testing with a Single Mean

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Lecture 10: Hypothesis Testing

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Lecture 11: The Chi-Square Distribution

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Unit 5 Outline

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Goodness-of-Fit Test Practice

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Contingency Tables Practice

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Test of Single Variance Practice

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Hypothesis Testing for Two Proportions Practice

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Single Mean, Known Pop. Std. Deviation Practice

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Hypothesis Testing for Two Averages Practice

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Single Mean, Unknown Std. Deviation Practice

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Single Proportion Practice

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Chapter 9: Hypothesis Testing

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Chapter 10: Hypothesis Testing

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Chapter 11: The Chi-Square Distribution

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5.1 Hypothesis Testing: Single Mean and Single Pro...

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5.2 Hypothesis Testing: Two Means, Paired Data, Tw...

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5.3 Chi-Square Distribution

### Unit 6: Correlation, Regr...

The unit description from Saylor.org: One of the main reasons you will conduct analysis is in order to understand how two variables are related to one another. The most common type of relationship is a linear relationship... Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. Regression, on the other hand, is the study of the strength of a linear relationship between an independent and dependent variable, and can be used to predict the value of the dependent variable when the value of the independent variable is unknown. Also, you will learn about a method called Analysis of Variance (abbreviated ANOVA), which is used for hypothesis tests involving more than two averages. ANOVA is about examining the amount of variability in the Y variable and trying to see where that variability is coming from.

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Covariance and the Regression Line

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ANOVA 1: Calculating SST (total sum of squares)

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ANOVA 2: Calculating SSW and SSB (total sum of squ...

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ANOVA 3: Hypothesis test with F-statistic

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Correlation and Causality

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Lecture 12: Linear Regression and Correlation

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Unit 6 Outline

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Linear Regression Practice

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ANOVA Practice

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Chapter 12: Linear Regression and Correlation

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Chapter 13: F Distribution and ANOVA

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6.1 Linear Regression

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6.2 Correlation

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6.3 F-Distribution and ANOVA