Introduction to Probability and Statistics

A college level first course in Statistics

(334 ratings)

994 students

Created by Dane McGuckian

Last updated 1/2019

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What you'll learn

Students will learn probability and basic techniques of data analysis and inference. Additionally, students will gain a deeper understanding of the underlying concepts.

Requirements

Basic Arithmetic and Algebra Skills

Description

This course will begin with an overview of data types and descriptive Statistics. There will be extensive coverage of probability topics along with an introduction to discrete and continuous probability distributions. The course ends with a discussion of the central limit theorem and coverage of estimation using confidence intervals and hypothesis testing. This course is equivalent to most college level Statistics I courses.

Who this course is for:

Students that are taking or would like to take an introductory course in Statistics in college or an AP course in high school will find this course useful.

8 sections • 96 lectures • 8h 24m total length

The Role of Statistics
01:11
Preview04:07
Identify a Statistical Population
5 questions
Preview03:10
The Reasons for Taking a Sample
4 questions
Preview07:35
Classifying Data
9 questions
Population Parameters Vs Sample Statistics
04:13
Parameters and Statistics
4 questions
Descriptive Statistics Vs Inferential Statistics
01:05
Simple Random Samples
00:47
Section 1 Mixed Practice
13 questions

Organizing and Presenting Data
01:50
Relative Frequency
03:02
Relative Frequency
2 questions
Histograms
04:54
Histograms
2 questions
Left-End-Point Convention
03:08
Simplifying an Expression in Summation Notation
06:01
Simplify an Expression Using Summation Notation
2 questions
Four Important Properties of the Mean
02:25
Four Important Properties of the Mean
4 questions
Identifying Situations Where the Mean, Median, and Mode Should be Used
08:30
Identify Situations Where the Mean, Median, and Mode Should be Used
6 questions
Categorize a Distribution as Either Left Skewed, Right Skewed, or Symmetric
04:11
Categorize a Distribution as Either Left Skewed, Right Skewed, or Symmetric
6 questions
The Role of Measures of Dispersion in Descriptive Statistics
01:38
Identify the Role of Measures of Dispersion in Descriptive Statistics
4 questions
Determine when the Range is an Appropriate Measure of Dispersion
04:58
Determine when the Range is an Appropriate Measure of Dispersion
5 questions
Standard Deviation and Variance
05:10
The Standard Deviation and Variance
6 questions
Calculate the Standard Deviation for a Set of Data
07:39
Calculate the Standard Deviation for a Set of Data
3 questions
Chebyshev’s Theorem
09:21
Chebyshev’s Theorem
4 questions
Preview05:05
Calculate the Minimum Percentage of Data Inside a Symmetric Interval
3 questions
Calculate the Maximum Percentage of Data Outside a Symmetric Interval
10:23
Calculate the Maximum Percentage of Data Outside a Symmetric Interval
3 questions
Create an Interval that Captures At Least 1-1k^2 of the Data
08:12
Create an Interval that Captures At Least 1-1k^2 of the Data
5 questions
The Empirical Rule
04:50
The Empirical Rule
6 questions
Form an Interval that Captures Approximately X% of the Data
Processing..
Form an Interval that Captures Approximately X% of the Data
3 questions
Use the Empirical Rule to determine the Percentage of Data Inside an Interval
05:57
Use the Empirical Rule to determine the Percentage of Data Inside an Interval
6 questions
Contrast the Use of Chebyshev's Theorem and the Empirical Rule
05:22
Contrast the Use of Chebyshev's Theorem and the Empirical Rule
6 questions
Calculate and Interpret Z-scores (as a Measure of Unusualness)
07:11
Calculate and Interpret Z-scores (as a Measure of Unusualness)
4 questions
Use Z Scores to Compare the Relative Standing of Two Measurements
06:57
Use Z Scores to Compare the Relative Standing of Two Measurements
6 questions
Mixed Practice Sections 1 and 2
29 questions

Preview06:02
Basic Probability Approach
3 questions
Know When to Assume Equally Likely Outcomes When Calculating Probability
01:31
Know When to Assume Equally Likely Outcomes When Calculating Probability
4 questions
Preview04:20
Calculate Basic Probability
5 questions
Explain the Law of Large Numbers
03:20
Explain the Law of Large Numbers
6 questions
Discuss the Minimum and Maximum Likelihood of an Event
04:32
Discuss the Minimum and Maximum Likelihood of an Event
4 questions
Interpret a Given Probability Value
01:29
Interpret a Given Probability Value
5 questions
Use the Fundamental Counting Rule to Determine the Number of Possible Outcomes
06:40
Use the Fundamental Counting Rule to Determine the Number of Possible Outcomes
7 questions
Define Combinations and the Factorial Operation
05:50
Define Combinations and the Factorial Operation
6 questions
Apply the Combinations Formula to Determine the Number of Possible Outcomes
03:05
Apply the Combinations Formula to Determine the Number of Possible Outcomes
5 questions
Contrast the Situations where It Is Appropriate to Use Combinations and Permutat
08:24
Contrast Situations where It Is Appropriate to Count Combinations & Permutations
6 questions
Contrast P(A ∪ B) and P(A ∩ B)
00:49
Contrast P(A ∪ B) and P(A ∩ B)
5 questions
Use the Addition Rule of Probability with and without a Contingency Table
05:14
Use the Addition Rule of Probability with and without a Contingency Table
9 questions
Contrast the Meaning of Mutually Exclusive Events and Independent Events
02:04
Contrast the Meaning of Mutually Exclusive Events and Independent Events
6 questions
Use the Addition Rule of Probability for Mutually Exclusive Events
07:38
Use the Addition Rule of Probability for Mutually Exclusive Events
5 questions
Interpret a Conditional Probability
02:27
Interpret a Conditional Probability
6 questions
Use the Conditional Rule of Probability Without a Contingency Table
04:24
Use the Conditional Rule of Probability Without a Contingency Table
6 questions
Use the Conditional Rule of Probability With a Contingency Table
03:21
Use the Conditional Rule of Probability With a Contingency Table
4 questions
Use the Multiplication Rule for Independent Events
05:58
Use the Multiplication Rule for Independent Events
4 questions
Use the Multiplication Rule for Dependent Events
05:49
Use the Multiplication Rule for Dependent Events
5 questions
Know the Approach to Calculate the Probability of At Least One of Something
10:35
Know the Approach to Calculate the Probability of At Least One of Something
4 questions
Calculate the Probability of At Least One of Something
06:44
Calculate the Probability of At Least One of Something
4 questions
Mixed Practice Section 3
18 questions

Probability Distributions for Discrete Random Variables
07:02
Probability Distributions for Discrete Random Variables
5 questions
Calculate and Interpret the Expected Value of a Discrete Random Variable
09:52
Calculate and Interpret the Expected Value of a Discrete Random Variable
4 questions
Calculate the Variance and Standard Deviation of a Discrete Random Variable
09:25
Calculate the Variance and Standard Deviation of a Discrete Random Variable
2 questions
The Characteristics of a Binomial Experiment & the Binomial Probability Formula
05:48
The Characteristics of a Binomial Experiment & the Binomial Probability Formula
5 questions
Calculate the Probability of X Successes in a Binomial Experiment
04:57
Calculate the Probability of X Successes in a Binomial Experiment
3 questions
Calculate the Probability of a Cumulative Set of Events for a Binomial Experimen
06:37
Calculate the Probability of a Cumulative Set of Events for a Binomial Experimen
3 questions
Calculate the Mean and Standard Deviation of a Binomial Random Variable
04:08
Calculate the Mean and Standard Deviation of a Binomial Random Variable
3 questions
Mixed Practice Section 3 and 4
18 questions

Traits of Continuous Random Variables
01:33
Traits of Continuous Random Variables
4 questions
Contrast Probability for Continuous Random Variables & Discrete Random Variables
03:06
Contrast Probability for Continuous Random Variables & Discrete Random Variables
3 questions
A Family of Normal Distributions
04:07
A Family of Normal Distributions
4 questions
Find Areas Under the Standard Normal Curve between the Mean and a Value
03:06
Find Areas Under the Standard Normal Curve between the Mean and a Value
4 questions
Areas Under the Standard Normal Curve Inside an Interval Surrounding the Mean
03:49
Areas Under the Standard Normal Curve Inside an Interval Surrounding the Mean
3 questions
Areas Under the Normal Curve between Two Values on the Same Side of the Mean
03:23
Areas Under the Normal Curve between Two Values on the Same Side of the Mean
3 questions
Areas Under the Standard Normal Curve between a Positive Z Value and Infinity
03:02
Areas Under the Standard Normal Curve between a Positive Z Value and Infinity
3 questions
Areas Under the Standard Normal Curve between a Negative Z Value and Infinity
02:13
Areas Under the Standard Normal Curve between a Negative Z Value and Infinity
3 questions
Calculate a Tail Area for a Non-Standard Normal Random Variable
04:07
Calculate a Tail Area for a Non-Standard Normal Random Variable
4 questions
Calculate the Probability a Normal Random Variable is Above-Average or Less
03:02
Calculate the Probability a Normal Random Variable is Above-Average or Less
3 questions
Probability a Normal Random Variable is Between Values that Surround the Mean
03:42
Probability a Normal Random Variable is Between Values that Surround the Mean
2 questions
Calculate the Probability a Normal Variable is Between Two Below Average Values
04:46
Calculate the Probability a Normal Variable is Between Two Below Average Values
3 questions
Calculate the Value Corresponding to an Upper Percentile of the Normal Curve
05:45
Calculate the Value Corresponding to an Upper Percentile of the Normal Curve
3 questions
Calculate the Value Corresponding to a Lower Percentile of the Normal Curve
05:25
Calculate the Value Corresponding to a Lower Percentile of the Normal Curve
3 questions
Mixed Practice Section 5
18 questions

Sampling Distributions and the Desired Traits of a Point Estimator
11:00
Sampling Distributions and the Desired Traits of a Point Estimator
5 questions
The Mean and Standard Error of the Sample Mean
07:49
The Mean and Standard Error of the Sample Mean
5 questions
The Central Limit Theorem
07:03
The Central Limit Theorem
7 questions
Applying the Central Limit Theorem
06:12
Applying the Central Limit Theorem
3 questions
Mixed Practice Sections 5 and 6
18 questions

Interval Estimators
10:35
Interval Estimators
3 questions
Finding Critical Z Values
05:38
Finding Critical Z Values
3 questions
Constructing a Large Sample Confidence Interval to Estimate a Mean
11:36
Constructing a Large Sample Confidence Interval to Estimate a Mean
5 questions
Determine the Sample Size Needed to Estimate a Mean
10:27
Determine the Sample Size Needed to Estimate a Mean
3 questions
Finding Critical t Values
07:12
Finding Critical t Values
3 questions
Constructing a Small Sample Confidence Interval to Estimate a Mean
08:03
Constructing a Small Sample Confidence Interval to Estimate a Mean
4 questions
The Sampling Distribution of the Sample Proportion
05:23
The Sampling Distribution of the Sample Proportion
3 questions
Constructing a Confidence Interval for the Population Proportion
07:12
Constructing a Confidence Interval for the Population Proportion
5 questions
Mixed Review for Section 7
12 questions

Properties of the Null and Alternative Hypotheses
04:45
Properties of the Null and Alternative Hypotheses
7 questions
Determine the Null and Alternative Hypothesis
05:22
Determine the Null and Alternative Hypothesis
4 questions
Test Statistics
04:01
Test Statistics
4 questions
Type I and Type II Errors
09:40
Type I and Type II Errors
5 questions
Reducing the Likelihood of a Type I Error
05:58
Reducing the Likelihood of a Type I Error
8 questions
Finding a Critical Value for a One-Tailed Hypothesis Test
04:03
Finding a Critical Value for a One-Tailed Hypothesis Test
2 questions
Express the Rejection Region for a Two-Tailed Hypothesis Test
05:12
Express the Rejection Region for a Two-Tailed Hypothesis Test
2 questions
The Classical Approach to a Large-Sample Hypothesis Test of the Population Mean
07:29
The Classical Approach to a Large-Sample Hypothesis Test of the Population Mean
2 questions
Rules for Calculating a P-Value
05:26
Rules for Calculating a P-Value
4 questions
Calculating a P-Value
04:01
Calculating a P-Value
4 questions
The P-Value Method of Hypothesis Testing
05:00
The P-Value Method of Hypothesis Testing
3 questions
Finding a t Critical Value for a Two-Tailed Hypothesis Test
02:51
Finding a t Critical Value for a Two-Tailed Hypothesis Test
2 questions
Small-Sample Hypothesis Tests about a Population Mean
04:50
Small-Sample Hypothesis Tests about a Population Mean
2 questions
Mixed Practice Sections 7 and 8
32 questions

Dane McGuckian

University Statistics Instructor

4.6 Instructor Rating
334 Reviews
994 Students
1 Course

Dane McGuckian has almost 20 years of experience helping students learn mathematics and statistics. For the past 13 years, he has taught Statistics full-time at the college level. He is a published author, and he owns two websites devoted to math and statistics instruction. Dane loves the challenge of making difficult concepts intuitive for new learners.

This course includes:

Training 5 or more people?

Introduction to Probability and Statistics

What you'll learn

Requirements

Description

Who this course is for:

Course content

Instructor

This course includes:

Training 5 or more people?

Introduction to Probability and Statistics

What you'll learn

Requirements

Description

Who this course is for:

Course content

Types of Data and an Intro to Statistics7 lectures • 22min

Descriptive Statistics22 lectures • 1hr 57min

Probability21 lectures • 1hr 40min

Discrete Random Variables7 lectures • 48min

Continuous Random Variables14 lectures • 51min

The Sampling Distribution of the Sample Mean4 lectures • 32min

One Sample Interval Estimators8 lectures • 1hr 6min

One Sample Hypothesis Tests13 lectures • 1hr 9min

Instructor