STATS-1: Statistics for Data Science 1

Topics covered

• Introduction & types of data

  • Types of data
  • Descriptive statistics
  • Inferential statistics
  • Scales of measurement

Expected skills: Classify data and distinguish descriptive from inferential questions.

Topics covered

• Describing categorical data

  • Frequency distributions
  • Graphing categorical data
  • Mode for categorical variables
  • Median for categorical variables

Expected skills: Summarize categorical data with suitable tables, graphs and measures.

Topics covered

• Describing numerical data

  • Frequency tables
  • Mean, median and mode
  • Quartiles and percentiles
  • Range and variance
  • Standard deviation
  • Interquartile range
  • Five-number summary

Expected skills: Calculate numerical summaries and compare measures of centre and spread.

Topics covered

• Association between two variables

  • Categorical associations
  • Relative frequencies
  • Contingency tables
  • Scatterplots
  • Covariance
  • Pearson correlation
  • Point-biserial correlation

Expected skills: Describe associations using tables, plots, covariance and correlation.

Topics covered

• Basic principles of counting

  • Addition rule
  • Multiplication rule
  • Factorials

Expected skills: Count outcomes using addition, multiplication and factorials.

Topics covered

• Permutations & combinations

  • Permutations
  • Combinations

Expected skills: Distinguish ordered arrangements from unordered selections.

Topics covered

• Probability

  • Basic definitions
  • Events
  • Properties of probability

Expected skills: Describe events and apply the basic rules of probability.

Topics covered

• Conditional probability

  • Multiplication rule
  • Independence
  • Law of total probability
  • Bayes’ theorem

Expected skills: Calculate conditional probabilities and distinguish independence from conditioning.

Topics covered

• Random variables

  • Random experiments
  • Sample spaces
  • Discrete random variables
  • Continuous random variables
  • Probability mass function
  • Cumulative distribution function

Expected skills: Use random variables, PMFs and CDFs to describe outcomes.

Topics covered

• Expectation & variance

  • Expectation of discrete random variables
  • Variance
  • Standard deviation

Expected skills: Compute expectation and variability of a discrete random variable.

Topics covered

• Binomial & Poisson random variables

  • Bernoulli trials
  • Independent identically distributed random variables
  • Binomial distribution
  • Expectation and variance of a binomial variable
  • Poisson distribution

Expected skills: Recognize binomial and Poisson models and interpret their parameters.

Topics covered

• Introduction to continuous random variables

  • Area under a curve
  • Properties of probability density functions
  • Uniform distribution
  • Exponential distribution

Expected skills: Use densities and areas to interpret probabilities for continuous variables.