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Learn MoreIntroduction to Probability and Statistics
Rating: 4.4 out of 54.4(1,884 ratings)
10,321 students
Introduction to Probability and Statistics
A college level first course in Statistics
Created byDane McGuckian
Last updated 8/2023
English
What you'll learn
- Students will learn probability and basic techniques of data analysis and inference. Students will gain a deeper understanding of the underlying concepts.
- Calculate the Probability of X Successes in a Binomial Experiment
- Construct a Confidence Interval for the Mean or Proportion
- Use the Classical Approach of Hypothesis Testing to Determine the Initial and Final Conclusion for a Test of Hypothesis
Explore related topics
Course content
8 sections • 97 lectures • 8h 29m total length
- The Role of Statistics1:12
- Population and Sample4:07
After watching this short video, you will be able to define the terms population and sample in the context of Statistics.
- Identify a Statistical Population
- Why Take a Sample of Data?3:10
After watching this video, you will understand why Statisticians often have to settle for a sample of data instead of working with the full set of population data.
- The Reasons for Taking a Sample
- Categorical Data and Numerical Data: Discrete Vs Continuous7:35
In this video, you will learn to categorize data as qualitative or quantitative. If quantitative, you will learn to distinguish between data that is discrete and data that is continuous.
- Classifying Data
- Population Parameters Vs Sample Statistics4:13
After viewing this video, you will be able to classify values as either population parameters or sample statistics.
- Parameters and Statistics
- Descriptive Statistics Vs Inferential Statistics1:05
- Simple Random Samples0:47
- Section 1 Mixed Practice
- Organizing and Presenting Data1:50
Descriptive statistics starts with organizing and presenting data in a way that helps us to see the big picture from the small details which are provided by a set of measurements.
- Relative Frequency3:02
This video introduces the concept of relative frequency, a simple and important idea.
- Relative Frequency
- Histograms4:54
In this video, we will discuss the best practices for creating a histogram.
- Histograms
- Left-End-Point Convention3:08
This video explains the left-end-point convention for histograms and frequency distributions.
- Simplifying an Expression in Summation Notation6:01
In this video, we will demonstrate the approach to evaluating an expression that uses summation notation.
- Simplify an Expression Using Summation Notation
- Four Important Properties of the Mean2:25
In this video, we will discuss four important properties of the mean.
- Four Important Properties of the Mean
- Identifying Situations Where the Mean, Median, and Mode Should be Used8:30
In this video, you will learn how to identify when to use each of the different measures of the center discussed: mean, median, and mode.
- Identify Situations Where the Mean, Median, and Mode Should be Used
- Categorize a Distribution as Either Left Skewed, Right Skewed, or Symmetric4:11
In this video, you will learn how to identify left skewed, right skewed, and symmetric distributions.
- Categorize a Distribution as Either Left Skewed, Right Skewed, or Symmetric
- The Role of Measures of Dispersion in Descriptive Statistics1:38
A discussion of measures of dispersion.
- Identify the Role of Measures of Dispersion in Descriptive Statistics
- Determine when the Range is an Appropriate Measure of Dispersion4:58
In this video, we will discuss the range as a measure of dispersion (or variation).
- Determine when the Range is an Appropriate Measure of Dispersion
- Standard Deviation and Variance5:10
In this video, you will learn how to derive the standard deviation from the variance.
- The Standard Deviation and Variance
- Calculate the Standard Deviation for a Set of Data7:39
In this video, you will learn how to calculate the sample standard deviation for a set of data.
- Calculate the Standard Deviation for a Set of Data
- Chebyshev’s Theorem9:21
In this video, you will be introduced to Chebyshev's theorem.
- Chebyshev’s Theorem
- Calculate the Minimum Percentage of Data Inside a Symmetric Interval5:05
In this video, you will learn how to use Chebyshev's theorem to calculate the minimum percentage of data inside an interval that has limits that are equidistant from the mean.
- Calculate the Minimum Percentage of Data Inside a Symmetric Interval
- Calculate the Maximum Percentage of Data Outside a Symmetric Interval10:23
In this video, you will learn how to use Chebyshev's theorem to calculate the maximum percentage of data outside an interval that has limits that are equidistant from the mean.
- Calculate the Maximum Percentage of Data Outside a Symmetric Interval
- Create an Interval that Captures At Least 1-1k^2 of the Data8:12
In this video, you will learn how to use Chebyshev's theorem to create an interval that captures some minimum proportion of a given data set.
- Create an Interval that Captures At Least 1-1k^2 of the Data
- The Empirical Rule4:50
In this video, you will learn a useful rule named the empirical rule.
- The Empirical Rule
- Form an Interval that Captures Approximately X% of the Data
In this video, you will learn how to use empirical rule to create an interval that captures some approximate proportion of a given data set.
- Form an Interval that Captures Approximately X% of the Data
- Use the Empirical Rule to determine the Percentage of Data Inside an Interval5:57
In this video, you will learn how to use empirical rule to calculate the approximate percentage of data inside a given interval.
- Use the Empirical Rule to determine the Percentage of Data Inside an Interval
- Contrast the Use of Chebyshev's Theorem and the Empirical Rule5:22
In this video, you will learn to distinguish between situations that require the use of Chebyshev's rule and situations that allow us to use the empirical rule.
- Contrast the Use of Chebyshev's Theorem and the Empirical Rule
- Calculate and Interpret Z-scores (as a Measure of Unusualness)7:11
In this video, you will learn how to calculate and interpret z-scores as a measure of unusualness.
- Calculate and Interpret Z-scores (as a Measure of Unusualness)
- Use Z Scores to Compare the Relative Standing of Two Measurements6:57
In this video, you will learn how to compare the relative standing of two measurements using z-scores.
- Use Z Scores to Compare the Relative Standing of Two Measurements
- Mixed Practice Sections 1 and 2
- Basic Probability6:02
In this lecture, you will learn two different ways to express the probability of some event, A.
- Basic Probability Approach
- Know When to Assume Equally Likely Outcomes When Calculating Probability1:31
Just because an experiment has k possible outcomes doesn't mean that the probability of each of those outcomes is 1/k. This short article reminds us to be careful about assuming equally likely outcomes for an experiment.
- Know When to Assume Equally Likely Outcomes When Calculating Probability
- Calculate Basic Probability4:20
In this video, we will demonstrate how to calculate the probability of an event from a given set of related data.
- Calculate Basic Probability
- Explain the Law of Large Numbers3:20
The law of large numbers says that the proportion of favorable outcomes for an event obtained from a large number of trials should be close to the expected proportion of favorable outcomes for the event. This observed proportion will move closer and closer to the expected proportion as the number of trials increases.
- Explain the Law of Large Numbers
- Discuss the Minimum and Maximum Likelihood of an Event4:32
The minimum likelihood of an event is zero, and the maximum likelihood of an event is 1. If expressed as a proportion, all probability values must be between 0 and 1 inclusive.
- Discuss the Minimum and Maximum Likelihood of an Event
- Interpret a Given Probability Value1:29
- Interpret a Given Probability Value
- Use the Fundamental Counting Rule to Determine the Number of Possible Outcomes6:40
To use the fundamental counting rule, you must complete the following steps:
1) break the process or experiment into steps or individual tasks.
2) determine the number of outcomes or possibilities for each individual step or ways to complete each individual task.
3) multiply all of the numbers obtained above. This is the number of possible outcomes for the original task (experiment or process).
- Use the Fundamental Counting Rule to Determine the Number of Possible Outcomes
- Define Combinations and the Factorial Operation5:50
In this video, you will learn how a combination is defined and the factorial operation will be introduced. Also, you will learn how to calculate the number of possible combinations of size r that can be drawn from a set of size n.
- Define Combinations and the Factorial Operation
- Apply the Combinations Formula to Determine the Number of Possible Outcomes3:05
This video demonstrates how to apply the combinations formula to count combinations.
- Apply the Combinations Formula to Determine the Number of Possible Outcomes
- Contrast the Situations where It Is Appropriate to Use Combinations and Permutat8:24
When attempting to solve a counting problem, answer the following three questions:
· Are we selecting a subset of r items from a set of n items?
· Is it true that the order of the r items in the subset does not matter?
· Are the selections made without replacement, which means repetition of items is not allowed?
If the answer to all three of these questions is yes, you should use the combinations formula to solve the problem. If you cannot answer yes to all three of the questions, you can use fundamental counting rule to solve the problem.
- Contrast Situations where It Is Appropriate to Count Combinations & Permutations
- Contrast P(A ∪ B) and P(A ∩ B)0:49
This short article discusses the difference between P(A ∪ B) and P(A ∩ B).
- Contrast P(A ∪ B) and P(A ∩ B)
- Use the Addition Rule of Probability with and without a Contingency Table5:14
In this video, you will learn to use the addition rule of probability to calculate the probability that, given a pair of events A and B, either event A or B occurs as the outcome of an experiment.
- Use the Addition Rule of Probability with and without a Contingency Table
- Contrast the Meaning of Mutually Exclusive Events and Independent Events2:04
This article compares and contrasts mutually exclusive events and independent events.
- Contrast the Meaning of Mutually Exclusive Events and Independent Events
- Use the Addition Rule of Probability for Mutually Exclusive Events7:38
In this video, you will learn to use the addition rule of probability to calculate the probability that, given a pair of mutually exclusive events A and B, either event A or B occurs.
- Use the Addition Rule of Probability for Mutually Exclusive Events
- Interpret a Conditional Probability2:27
In this article, we will discuss interpreting conditional probability.
- Interpret a Conditional Probability
- Use the Conditional Rule of Probability Without a Contingency Table4:24
In this video, you will learn to calculate a conditional probability without the use of a contingency table. To calculate the probability that an event (A) occurs, given that some other event (B) has occurred, we divide the probability that both of the events occur (A and B) together by the probability that the given event (B) occurs.
- Use the Conditional Rule of Probability Without a Contingency Table
- Use the Conditional Rule of Probability With a Contingency Table3:21
In this video, you will learn to calculate a conditional probability with the help of a contingency table.
- Use the Conditional Rule of Probability With a Contingency Table
- Use the Multiplication Rule for Independent Events5:58
In this video, we demonstrate the use of the multiplication rule of probability for independent events.
- Use the Multiplication Rule for Independent Events
- Use the Multiplication Rule for Dependent Events5:49
In this video, we demonstrate the use of the multiplication rule of probability for dependent events.
- Use the Multiplication Rule for Dependent Events
- Know the Approach to Calculate the Probability of At Least One of Something10:35
In this video, we demonstrate the use of complements to find a probability.
- Know the Approach to Calculate the Probability of At Least One of Something
- Calculate the Probability of At Least One of Something6:44
In this video, we find the probability of an event by first calculating its complement and then subtracting the result from one.
- Calculate the Probability of At Least One of Something
- Mixed Practice Section 3
- Probability Distributions for Discrete Random Variables7:02
In this video, you'll learn to contrast discrete random variables and continuous random variables, to define a probability distribution of a discrete random variable, and to describe the characteristics of a probability distribution.
- Probability Distributions for Discrete Random Variables
- Calculate and Interpret the Expected Value of a Discrete Random Variable9:52
After watching this video you will learn the formula for the mean of a discrete probability distribution and how to calculate (and interpret) the expected value of a discrete random variable.
- Calculate and Interpret the Expected Value of a Discrete Random Variable
- Calculate the Variance and Standard Deviation of a Discrete Random Variable9:25
In this video, you learn the formula for the variance and standard deviation of a discrete random variable, how to calculate the variance and standard deviation of a discrete random variable, and how to determine if an event is unusual using the mean and standard deviation of a random variable.
- Calculate the Variance and Standard Deviation of a Discrete Random Variable
- The Characteristics of a Binomial Experiment & the Binomial Probability Formula5:48
In this video, you will learn to identify the five characteristics of a binomial experiment and to recognize the binomial probability formula.
- The Characteristics of a Binomial Experiment & the Binomial Probability Formula
- Calculate the Probability of X Successes in a Binomial Experiment4:57
In this video, you will learn how to calculate the probability of x successes in n trials of a binomial experiment.
- Calculate the Probability of X Successes in a Binomial Experiment
- Calculate the Probability of a Cumulative Set of Events for a Binomial Experimen6:37
In this video, you will learn how to calculate the probability of a cumulative set of events of a binomial experiment.
- Calculate the Probability of a Cumulative Set of Events for a Binomial Experimen
- Calculate the Mean and Standard Deviation of a Binomial Random Variable4:08
In this video, you will learn to recognize the formula for the mean and standard deviation of a binomial random variable and how to calculate the mean, standard deviation, and variance of a binomial random variable.
- Calculate the Mean and Standard Deviation of a Binomial Random Variable
- Mixed Practice Section 3 and 4
- Traits of Continuous Random Variables1:33
In this video, we describe the traits of continuous random variables.
- Traits of Continuous Random Variables
- Contrast Probability for Continuous Random Variables & Discrete Random Variables3:06
In this video, we compare and contrast discrete probability distributions and continuous probability distributions.
- Contrast Probability for Continuous Random Variables & Discrete Random Variables
- A Family of Normal Distributions4:07
In this video, we discuss the normal probability distribution and the standard normal probability distribution.
- A Family of Normal Distributions
- Find Areas Under the Standard Normal Curve between the Mean and a Value3:06
In this video, we learn to use a z table to find the probability that z is between 0 and some given z score.
- Find Areas Under the Standard Normal Curve between the Mean and a Value
- Areas Under the Standard Normal Curve Inside an Interval Surrounding the Mean3:49
In this video, we learn to use a z table to find the probability that a z value falls between two given values that surround the mean of zero.
- Areas Under the Standard Normal Curve Inside an Interval Surrounding the Mean
- Areas Under the Normal Curve between Two Values on the Same Side of the Mean3:23
In this video, we use a z table to find the probability that a z value falls between two z values that are either both above the mean or both below the mean.
- Areas Under the Normal Curve between Two Values on the Same Side of the Mean
- Areas Under the Standard Normal Curve between a Positive Z Value and Infinity3:02
In this video, we learn how to use a z table to find the probability that a z value falls into one of the tails of the z distribution beyond some given z value.
- Areas Under the Standard Normal Curve between a Positive Z Value and Infinity
- Areas Under the Standard Normal Curve between a Negative Z Value and Infinity2:13
In this video, we use a z table to find the probability that a z value is greater than a given negative z value.
- Areas Under the Standard Normal Curve between a Negative Z Value and Infinity
- Calculate a Tail Area for a Non-Standard Normal Random Variable4:07
In this video, we use a z table to calculate the probability that a non-standard normal random variable falls into the tail of the distribution beyond some given value.
- Calculate a Tail Area for a Non-Standard Normal Random Variable
- Calculate the Probability a Normal Random Variable is Above-Average or Less3:02
In this video, we use a z table to find the probability that a non-standard random variable falls below a given above-average value.
- Calculate the Probability a Normal Random Variable is Above-Average or Less
- Probability a Normal Random Variable is Between Values that Surround the Mean3:42
In this video, we learn to use a z table to find the probability that a non-standard normal random variable falls between two given values that surround the mean.
- Probability a Normal Random Variable is Between Values that Surround the Mean
- Calculate the Probability a Normal Variable is Between Two Above Average Values4:46
In this video, we use a z table to find the probability that a non-standard normal random variable falls between two values that are either both above the mean or both below the mean.
- Calculate the Probability a Normal Variable is Between Two Below Average Values
- Calculate the Value Corresponding to an Upper Percentile of the Normal Curve5:45
In this video, we learn to use a z table to find the measurement associated with an upper percentile of a normal probability distribution.
- Calculate the Value Corresponding to an Upper Percentile of the Normal Curve
- Calculate the Value Corresponding to a Lower Percentile of the Normal Curve5:25
In this video, we learn to use a z table to find the measurement associated with an lower percentile of a normal probability distribution.
- Calculate the Value Corresponding to a Lower Percentile of the Normal Curve
- Mixed Practice Section 5
- Sampling Distributions and the Desired Traits of a Point Estimator11:00
In this video, we discuss the desired traits of a point estimator, and the concept of a sampling distribution.
- Sampling Distributions and the Desired Traits of a Point Estimator
- The Mean and Standard Error of the Sample Mean7:49
In this video, we discuss the mean and standard deviation of the sampling distribution for the sample mean.
- The Mean and Standard Error of the Sample Mean
- The Central Limit Theorem7:03
In this video, we discuss a very important theorem in statistics called the central limit theorem.
- The Central Limit Theorem
- Applying the Central Limit Theorem6:12
In this video, we demonstrate the use of the central limit theorem.
- Applying the Central Limit Theorem
- Mixed Practice Sections 5 and 6
- Interval Estimators10:35
In this video, we introduce the concept of an interval estimator and discuss the idea of a confidence coefficient.
- Interval Estimators
- Finding Critical Z Values5:38
In this video, we discuss methods for finding critical z values, which are needed to construct large sample confidence intervals.
- Finding Critical Z Values
- Constructing a Large Sample Confidence Interval to Estimate a Mean11:36
In this video, we demonstrate how to calculate the margin of error and to construct a confidence interval for a mean.
- Constructing a Large Sample Confidence Interval to Estimate a Mean
- Determine the Sample Size Needed to Estimate a Mean10:27
In this video, we discuss factors affecting the size of the margin of error of a confidence interval, and we demonstrate how to calculate the sample size needed to estimate a population mean.
- Determine the Sample Size Needed to Estimate a Mean
- Finding Critical t Values7:12
In this video, we discuss methods for finding critical t values, which are needed to construct small sample confidence intervals.
- Finding Critical t Values
- Constructing a Small Sample Confidence Interval to Estimate a Mean8:03
In this video, we demonstrate how to calculate the margin of error and to construct a confidence interval for a mean when using a small sample size.
- Constructing a Small Sample Confidence Interval to Estimate a Mean
- The Sampling Distribution of the Sample Proportion5:23
In this video, we discuss the expected value of the sample proportion and the standard error of the sample proportion.
- The Sampling Distribution of the Sample Proportion
- Constructing a Confidence Interval for the Population Proportion7:12
In this video, we construct a confidence interval to estimate a population proportion.
- Constructing a Confidence Interval for the Population Proportion
- Mixed Review for Section 7
- Properties of the Null and Alternative Hypotheses4:45
In this video, we introduce the null and alternative hypotheses and discuss their properties.
- Properties of the Null and Alternative Hypotheses
- Determine the Null and Alternative Hypothesis5:22
In this video, we demonstrate how to determine the null and alternative hypotheses from a given claim.
- Determine the Null and Alternative Hypothesis
- Test Statistics4:01
In this video, we describe the logic of a test statistic and demonstrate how to calculate a test statistic from collected data.
- Test Statistics
- Type I and Type II Errors9:40
In this video, we discuss the four possible outcomes of a hypothesis test, and we define type I and type II errors.
- Type I and Type II Errors
- Reducing the Likelihood of a Type I Error5:58
In this video, we discuss the likelihood of committing a type I error, and we discuss ways to lower the likelihood of the type I error.
- Reducing the Likelihood of a Type I Error
- Finding a Critical Value for a One-Tailed Hypothesis Test4:03
In this video, we find the critical value for a one-tailed hypothesis test, and we determine a rejection region for the test.
- Finding a Critical Value for a One-Tailed Hypothesis Test
- Express the Rejection Region for a Two-Tailed Hypothesis Test5:12
In this video, we find the critical values for a two-tailed hypothesis test, and we determine a rejection region for the test.
- Express the Rejection Region for a Two-Tailed Hypothesis Test
- The Classical Approach to a Large-Sample Hypothesis Test of the Population Mean7:29
In this video, we use the classical approach to hypothesis testing to test a hypothesis about a population mean.
- The Classical Approach to a Large-Sample Hypothesis Test of the Population Mean
- Lecture 91.1 The liklihood of a Type I Error5:04
This short video goes over the rule(s) for determining the probability of a Type I error in hypothesis testing.
- Rules for Calculating a P-Value5:26
In this video, we define p-values, and we discuss the approach to calculating p-values from a test stat under three different conditions.
- Rules for Calculating a P-Value
- Calculating a P-Value4:01
In this video, we demonstrate how to calculate p-values.
- Calculating a P-Value
- The P-Value Method of Hypothesis Testing5:00
In this video, we use the p-value method to conduct a large sample hypothesis test about a population mean.
- The P-Value Method of Hypothesis Testing
- Finding a t Critical Value for a Two-Tailed Hypothesis Test2:51
In this video, we find the critical values for a two-tailed, small-sample hypothesis test, and we determine a rejection region for the test.
- Finding a t Critical Value for a Two-Tailed Hypothesis Test
- Small-Sample Hypothesis Tests about a Population Mean4:50
In this video, we demonstrate how to conduct a small-sample hypothesis test about a population mean.
- Small-Sample Hypothesis Tests about a Population Mean
- Mixed Practice Sections 7 and 8
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.