Duration of the online course: 16 hours and 30 minutes
New
Build real-world data skills with a free online statistics course: interpret graphs, calculate probability, and make confident decisions with practice and quizzes.
In this free course, learn about
Core statistical terms: population, sample, parameters vs statistics, and study goals
Classify data (qualitative/quantitative; discrete/continuous) and critique published studies
Design studies: observational vs experiments, stratified sampling, bias, and confounding
Build frequency distributions; display data with bar/pie charts, histograms; spot misleading graphs
Compute/interpret center & spread: mean, median, mode, range, variance, standard deviation
Use relative position tools: percentiles, z-scores, 5-number summary, box plots, IQR
Apply probability rules: addition, multiplication, complements; solve coin/die/card problems
Use counting methods: permutations, combinations, and structured counting practice problems
Work with discrete distributions: expected value, variance/SD; binomial, Poisson, hypergeometric
Normal distribution skills: areas/probabilities, z and inverse z; normal approx to binomial
Central Limit Theorem for means & proportions; conditions for normal approximation
Construct confidence intervals for means/proportions; choose z vs t and check assumptions
Hypothesis testing framework: H0/Ha, p-values, alpha, Type I/II errors; tests for means/proportions
Correlation & regression: Pearson r significance, LSRL, R², prediction/CI for slope; multiple regression
About the free online course
Applied Statistics gives you the tools to make sense of data and turn numbers into clear, defensible conclusions. Whether you are preparing for school assessments or want stronger analytical skills for work, this free online course helps you move beyond memorizing formulas and toward understanding what results mean in real situations.
You will start by learning how statisticians describe and classify data, how studies are designed, and why sampling methods matter. From there, you will get comfortable organizing information using frequency distributions and visual displays, then learn to spot common ways graphs can mislead. As you practice measures of center and spread, you will see how choices like mean versus median can change the story, especially when outliers or skewed distributions appear.
Probability becomes a practical decision-making toolkit as you learn the addition and multiplication rules, as well as counting methods like permutations and combinations. Those ideas connect directly to widely used probability models, helping you recognize when a situation fits binomial, Poisson, or hypergeometric reasoning and how expected value and variance describe outcomes over time.
The course then builds toward inference, where many learners feel statistics becomes truly useful. You will work with normal distributions and z-scores, understand what area under the curve represents, and use the central limit theorem to justify why sample results can be generalized. Confidence intervals and hypothesis tests are explained as structured ways to estimate and evaluate claims, including cases with known or unknown variation, comparisons between two groups, and paired data.
Finally, you will connect statistics to relationships in data through correlation and regression, learning how models can support prediction and how to interpret measures like R-squared responsibly. Throughout, targeted exercises reinforce each idea so you develop accuracy, intuition, and the confidence to critique studies, communicate findings, and apply statistical thinking in everyday and academic contexts.
Course content
Video class: Statistics - 1.1 Intro to Statistics13m
Exercise: In the context of statistics, which of the following statements best describes a parameter?
Video class: Statistics - 1.2 Classifying Data14m
Exercise: How can data be classified based on its nature?
Video class: Statistics - 1.3.1 Introduction to Statistical Studies08m
Exercise: In a statistical study aiming to analyze the impact of a new fertilizer on plant growth, what is the primary goal of the study?
Video class: Statistics - 1.3.2 Observational Studies12m
Exercise: Which of the following best describes a stratified sampling method?
Video class: Statistics - 1.3.3 Experiments12m
Exercise: What is the key feature that differentiates experiments from observational studies?
Video class: Statistics - 1.4 Critiquing a Published Study06m
Exercise: What should you evaluate when critiquing a published study?
Video class: Statistics - 2.1 Frequency Distributions19m
Exercise: Which of the following is true about frequency distributions?
Video class: Statistics - 2.2.1 Displaying Qualitative Data09m
Exercise: What is the correct process to find the central angle for a pie chart?
Video class: Statistics - 2.2.2 Displaying Quantitative Data13m
Exercise: What type of display shows quantitative data using a continuous number line and bars that represent frequency for each range of values?
Video class: Statistics - 2.3 Analyzing Graphs06m
Exercise: What is an example of a misleading graph feature?
Video class: Statistics - 3.1 Measures of Center20m
Exercise: Which measure of center should be used when dealing with skewed data that contains outliers?
Video class: Statistics - 3.2.1 Measures of Spread or Dispersion16m
Exercise: Understanding Measures of Spread: Range and Standard Deviation
Video class: Statistics - 3.2.2 Empirical Rule and Chebyshev's Theorem10m
Exercise: The empirical rule describes the distribution of values in a normal distribution. If a normal distribution has a mean of 500 and a standard deviation of 100, what percentage of data would fall between 400 and 600?
Video class: Statistics - 3.3.1 Measures of Relative Position16m
Exercise: What is the 20th percentile in a dataset of 135 values?
Video class: Statistics - 3.3.2 Box Plots and the 5-Number Summary13m
Exercise: When interpreting a box plot, what does the interquartile range (IQR) represent?
Video class: Statistics - 3.3.3 Intro to Z-Scores12m
Exercise: How is a z-score calculated?
Video class: Statistics - 4.1 Intro to Probability20m
Exercise: What is the probability that in two coin tosses, at least one of them comes up heads?
Video class: Statistics - 4.2 Addition Rule for Probability20m
Exercise: What is the probability of rolling either a 3 or a 2 using a six-sided die?
Video class: Statistics - 4.3 Multiplication Rule for Probability16m
Exercise: What is the probability of drawing two face cards with replacement?
Video class: Statistics - 4.4 Permutations and Combinations19m
Exercise: How many permutations can be made with three friends if the order matters?
Video class: Statistics - 4.5 Probability and Counting Practice14m
Exercise: A teacher wants to arrange books on a shelf using the rules of permutations and combinations. They have 5 different mathematics books and 3 different science books. The teacher wishes to arrange 4 mathematics books and all 3 science books. In how many different ways can the teacher arrange these books if the mathematics books must stay together?
Video class: Statistics - 5.1.1 Expected Value of Discrete Probability Distributions16m
Video class: Statistics - 5.1.2 Variance and Standard Deviation of Discrete Probability Distributions05m
Exercise: When calculating the variance of a discrete probability distribution, what step involves adjusting each value relative to the mean before applying the probability?
Video class: Statistics - 5.2 The Binomial Distribution22m
Video class: Statistics - 5.3 The Poisson Distribution12m
Exercise: In a city park, a fountain averages 3 burst sprays every hour. What is the probability that in two hours, the fountain will spray exactly 8 burst sprays?
Video class: Statistics - 5.4.1 The Hypergeometric Distribution12m
Video class: Statistics - 5.4.2 Binomial, Poisson or Hypergeometric?06m
Exercise: Which distribution is best suited for calculating the probability of a website receiving a certain number of views in a fixed period, given the average views per week?
Video class: Statistics - 6.1 The Normal Distribution and Z-Scores11m
Video class: Statistics - 6.2 Area Under a Normal Distribution19m
Exercise: In the context of normal distributions, what does the area under the curve represent?
Video class: Statistics - 6.3 Probabilities in a Normal Distribution18m
Video class: Statistics - 6.4 Z-Scores in Reverse16m
Exercise: In a normal distribution, if the mean is 100 and the standard deviation is 15, what is the z-score for a raw score of 115?
Video class: Statistics - 6.5 Approximating a Binomial Distribution With a Normal Distribution18m
Video class: Statistics - 7.1 The Central Limit Theorem09m
Exercise: According to the central limit theorem, under what condition can the sampling distribution of the sample mean be approximated to a normal distribution when the population distribution is not normal?
Video class: Statistics - 7.2 The Central Limit Theorem with Means25m
Video class: Statistics - 7.3 The Central Limit Theorem with Proportions15m
Exercise: In applying the central limit theorem to proportions, what condition must be met for the theorem to be applicable?
Video class: Statistics - 8.1.1 An Introduction to Confidence Intervals08m
Video class: Statistics - 8.1.2 Estimating Population Means (? known)19m
Exercise: Suppose you are constructing a 95% confidence interval for the mean number of books read per year by a population of students. The population standard deviation is known to be 3 books, and a random sample of 50 students shows a mean of 20 books. Which of the following is the critical value (z-score) used to determine the margin of error for this confidence interval?
Video class: Statistics - 8.1.3 Calculations With Estimating Population Means - Sigma Known08m
Video class: Statistics - 8.2 Student's t-Distribution13m
Exercise: When using the Student's t-distribution, which of the following is true regarding the shape of the distribution as the degrees of freedom increase?
Video class: Statistics - 8.3 Estimating Population Means (Unknown)15m
Video class: Statistics - 8.4.1 Estimating Population Proportions11m
Exercise: When estimating population proportions using confidence intervals, which condition must be met for the sample size?
Video class: Statistics - 8.4.2 Calculations With Estimating Population Proportions09m
Video class: Statistics - 9.1 Comparing Two Population Means (? Known)19m
Exercise: In applied statistics, when attempting to compare the study habits between two independent groups of students, which of the following statements is correct regarding the use of confidence intervals to determine differences in mean study times?
Video class: Statistics - 9.2.1 Comparing Two Population Means (Unknown, Unequal Variances)14m
Video class: Statistics - 9.2.2 Comparing Two Population Means (Unknown, Equal Variances)13m
Exercise: When comparing two population means with unknown population standard deviations and assuming equal variances, which of the following statements is true for calculating the degrees of freedom in a t-distribution?
Video class: Statistics - 9.3 Comparing Two Population Means (Sigma Unknown, Dependent/Paired)12m
Video class: Statistics - 9.4 Comparing Two Population Proportions09m
Exercise: When comparing two population proportions, which condition must be met to use the z-model for estimation?
Video class: Statistics - 10.1.1 Introduction to Hypothesis Testing19m
Video class: Statistics - 10.1.2 Writing Hypotheses07m
Exercise: When formulating hypotheses for hypothesis testing, which of the following best describes the null hypothesis?
Video class: Statistics - 10.1.3 Interpreting Conclusions to Hypothesis Tests05m
Video class: Statistics - 10.1.4 Errors in Hypothesis Testing07m
Exercise: In the context of hypothesis testing, what is typically denoted by the letter alpha (α)?
Video class: Statistics - 10.2.1 Hypothesis Testing for Population Means (? known) - Right-Tailed20m
Video class: Statistics - 10.2.2 Hypothesis Testing for Population Means (? known) - Left-Tailed08m
Exercise: A researcher claims that the mean age of women at the time of their first marriage is lower than 26.5 years. A simple random sample of 213 newlywed women shows a mean age of 26.3 years. Assuming the population standard deviation is 2.3 years, and using a 90% confidence level, what is the conclusion of the hypothesis test with respect to the researcher's claim?
Video class: Statistics - 10.2.3 Hypothesis Testing for Population Means (? known) - 2-Tailed13m
Video class: Statistics - 10.3.1 Hypothesis Testing for Population Means (? unknown) - 1-Tailed20m
Exercise: When conducting a hypothesis test for population means where the population standard deviation (sigma) is unknown, which distribution model is used?
Video class: Statistics - 10.3.2 Hypothesis Testing for Population Means (? unknown) - 2-Tailed09m
Video class: Statistics - 10.4.1 Hypothesis Testing for Population Proportions - 1-Tailed17m
Exercise: What is the correct decision to make when the p-value is greater than the alpha level in a one-tailed hypothesis test for population proportions?
Video class: Statistics - 10.4.2 Hypothesis Testing for Population Proportions - 2-Tailed09m
Video class: Statistics - 11.1.1 Hypothesis Testing for 2 Sample Means (? known) - 1-Tailed22m
Exercise: What is the main focus of hypothesis testing in chapter 11 when dealing with two samples?
Video class: Statistics - 11.1.2 Hypothesis Testing for 2 Sample Means (? known) - 2-Tailed08m
Video class: Statistics - 11.2.1 Hypothesis Testing for 2 Sample Means (? unknown) - Unequal Variances12m
Exercise: In a hypothesis test involving two sample means with unknown and unequal variances, which of the following statements is true?
Video class: Statistics - 11.2.2 Hypothesis Testing for 2 Sample Means (? unknown) - Equal Variances13m
Video class: Statistics - 11.3 Hypothesis Testing for 2 Sample Means - Paired15m
Exercise: In hypothesis testing for two sample means with paired data, what is the test statistic formula when calculating the t-score for paired differences?
Video class: Statistics - 11.4 Hypothesis Testing for 2 Sample Proportions23m
Video class: Statistics - 12.1.1 Scatter Plots and Correlation19m
Exercise: In analyzing a scatter plot of two quantitative variables, which of the following best describes a positive correlation?
Video class: Statistics - 12.1.2 Determining Statistical Significance for the Pearson Correlation Coefficient16m
Video class: Statistics - 12.2.1 The Least Squares Regression Line (LSRL)10m
Exercise: What is the purpose of the least squares regression line in statistics?
Video class: Statistics - 12.2.2 Predicting With and Interpreting Values of the LSRL09m
Video class: Statistics - 12.2.3 Creating and Analyzing a Linear Regression Model05m
Exercise: In a study analyzing the relationship between average monthly temperature and monthly precipitation totals, a linear regression model was created with the equation ŷ = -15.424 + 0.225x. The coefficient of determination (R²) was calculated to be 0.7382. Which of the following interpretations of R² is correct?
Video class: Statistics - 12.3.1 Prediction Intervals for Linear Regression16m
Video class: Statistics - 12.3.2 Confidence Intervals for ?0 and ?105m
Exercise: In understanding the process of constructing a 95% confidence interval for the slope in a simple linear regression, which variables are typically involved?
Video class: Statistics - 12.4 Multiple Regression09m
