Introduction to Statistics

Complete syllabus

Every chapter and lesson

1. 01

   Chapter 1 · 3 lessons

   Describing Data

   1. 1.1

      Variables & types of data

      8 min · Quick check

      Lesson goal: By the end you can identify and differentiate between various types of variables and data.

      • Define variables and their importance in statistics.
      • Identify different types of data: qualitative and quantitative.
      • Differentiate between discrete and continuous data.
      • Understand the role of nominal and ordinal scales in categorizing data.
   2. 1.2

      Center & spread

      9 min · Quick check

      Lesson goal: By the end you can calculate and interpret measures of center and spread.

      • Define measures of center: mean, median, and mode.
      • Calculate the mean, median, and mode for a given data set.
      • Define measures of spread: range, variance, and standard deviation.
      • Calculate the range, variance, and standard deviation for a given data set.
   3. 1.3

      Distributions & shape

      8 min · Quick check

      Lesson goal: By the end you can describe and analyze the shape of distributions.

      • Define distribution and its significance in statistics.
      • Identify different types of distributions: normal, skewed, and uniform.
      • Understand the concept of skewness and kurtosis in describing shape.
      • Analyze graphical representations of data to determine distribution shape.
2. 02

   Chapter 2 · 3 lessons

   Probability

   1. 2.1

      Basic probability rules

      9 min · Quick check

      Lesson goal: By the end you can explain the basic rules of probability and how they apply to simple events.

      • Define probability and its significance in statistics.
      • Explain the addition rule for mutually exclusive events.
      • Describe the multiplication rule for independent events.
      • Illustrate the concept of complementary events.
   2. 2.2

      Conditional probability

      9 min · Quick check

      Lesson goal: By the end you can calculate and interpret conditional probabilities in various contexts.

      • Define conditional probability and its notation.
      • Explain the concept of dependent and independent events.
      • Apply Bayes' theorem to solve problems involving conditional probabilities.
   3. 2.3

      Random variables & expected value

      8 min · Quick check

      Lesson goal: By the end you can identify random variables and calculate their expected values.

      • Define random variables and distinguish between discrete and continuous types.
      • Explain the concept of expected value and its significance.
      • Calculate the expected value for simple random variables.
3. 03

   Chapter 3 · 3 lessons

   Distributions

   1. 3.1

      The normal distribution

      9 min · Quick check

      Lesson goal: By the end you can describe the characteristics and properties of the normal distribution.

      • Define the normal distribution and its significance in statistics.
      • Identify the key features of the normal distribution, including mean, median, and mode.
      • Explain the empirical rule and its application to normal distributions.
   2. 3.2

      The binomial distribution

      8 min · Quick check

      Lesson goal: By the end you can explain the binomial distribution and its applications.

      • Define the binomial distribution and its parameters: number of trials and probability of success.
      • Identify scenarios where the binomial distribution is applicable.
      • Calculate probabilities using the binomial probability formula.
   3. 3.3

      Sampling distributions & the CLT

      9 min · Quick check

      Lesson goal: By the end you can understand sampling distributions and the Central Limit Theorem (CLT).

      • Define sampling distribution and its importance in inferential statistics.
      • Explain the Central Limit Theorem and its implications for sample means.
      • Discuss how sample size affects the shape of the sampling distribution.
4. 04

   Chapter 4 · 3 lessons

   Estimation

   1. 4.1

      Point estimates & sampling error

      8 min · Quick check

      Lesson goal: By the end you can explain point estimates and the concept of sampling error.

      • Define point estimates and their role in statistics.
      • Explain sampling error and its implications for statistical analysis.
      • Discuss the relationship between sample size and sampling error.
   2. 4.2

      Confidence intervals for a mean

      9 min · Quick check

      Lesson goal: By the end you can calculate and interpret confidence intervals for a mean.

      • Define confidence intervals and their significance in statistics.
      • Explain how to calculate a confidence interval for a mean.
      • Interpret the meaning of a confidence interval in the context of data.
   3. 4.3

      Confidence intervals for a proportion

      8 min · Quick check

      Lesson goal: By the end you can calculate and interpret confidence intervals for a proportion.

      • Define confidence intervals for proportions and their importance.
      • Explain the steps to calculate a confidence interval for a proportion.
      • Interpret the results of a confidence interval for a proportion in real-world scenarios.
5. 05

   Chapter 5 · 3 lessons

   Hypothesis Testing

   1. 5.1

      The logic of significance

      9 min · Quick check

      Lesson goal: By the end you can explain the logic behind statistical significance in hypothesis testing.

      • Define statistical significance and its importance in hypothesis testing.
      • Explain the concept of the null hypothesis and alternative hypothesis.
      • Discuss the role of p-values in determining significance.
      • Describe the threshold for significance commonly used in research.
   2. 5.2

      Tests for means (t-tests)

      9 min · Quick check

      Lesson goal: By the end you can perform t-tests to compare means between groups.

      • Define t-tests and their purpose in hypothesis testing.
      • Identify the types of t-tests: independent, paired, and one-sample.
      • Explain the assumptions underlying t-tests.
      • Demonstrate how to calculate and interpret t-test results.
   3. 5.3

      Errors & common pitfalls

      8 min · Quick check

      Lesson goal: By the end you can identify common errors and pitfalls in hypothesis testing.

      • Define Type I and Type II errors in hypothesis testing.
      • Discuss the implications of statistical power and sample size.
      • Identify common misconceptions about p-values.
      • Explain the importance of proper study design to avoid errors.
6. 06

   Chapter 6 · 3 lessons

   Relationships

   1. 6.1

      Correlation

      8 min · Quick check

      Lesson goal: By the end you can explain the concept of correlation and its significance in statistics.

      • Define correlation and its purpose in statistical analysis.
      • Differentiate between positive, negative, and zero correlation.
      • Understand the correlation coefficient and its interpretation.
   2. 6.2

      Simple linear regression

      9 min · Quick check

      Lesson goal: By the end you can apply simple linear regression to analyze relationships between variables.

      • Define simple linear regression and its components.
      • Understand how to interpret the slope and intercept of the regression line.
      • Learn how to calculate and interpret the coefficient of determination.
   3. 6.3

      Chi-square for categorical data

      8 min · Quick check

      Lesson goal: By the end you can perform a Chi-square test for categorical data to assess relationships.

      • Define the Chi-square test and its application in analyzing categorical data.
      • Understand the null hypothesis in the context of the Chi-square test.
      • Learn how to calculate the Chi-square statistic and interpret the results.