S1 Tutorials

Collecting Data

Understanding population, census and samples

  1. Understanding Population, census and sample
  2. Random Sampling Methods
  3. Non Random Sampling methods

Representing Data

Mean

  1. Mean for discrete data
  2. Calculating the mean from a frequency table
  3. Exam Questions - Discrete data / mean

Median and Quartiles

  1. Median, lower, upper quartiles and interquartile range for discrete data
  2. Exam Questions - Median, lower, upper quartiles and interquartile range for discrete data
  3. Cumulative frequency curves
  4. How to interpret class intervals
  5. Estimating the median, quartiles, percentiles from a grouped frequency table
  6. Exam Questions - Estimating the median from a grouped frequency table
  7. Exam Questions - Estimating the median from a histogram

Skewness

  1. Types of skewness by comparing the mean with the median or quartiles

Standard Deviation

  1. Standard deviation
  2. Exam Questions - Discrete data / standard deviation
  3. Exam Questions - Continuous data / standard deviation

Statistical Diagrams

  1. Stem and leaf diagrams
  2. Box and whisker plots
  3. Exam Questions - Stem and leaf diagrams and box and whisker plots
  4. Histograms
  5. Exam Questions - Histograms
  6. Histograms - How to find the width and height of a class interval
  7. Exam Questions - Histograms, Finding the length and width of a rectangle

Permutations and Combinations

Permutations and Combinations

  1. Permutations of n different items
  2. Permutations of r items from n different items
  3. Permutations of repeated letters in a word
  4. Permutations with restrictions: letters / items together
  5. Permutations with restrictions : items at the ends
  6. Permutations with restrictions : items must not be together
  7. Combinations of n different items
  8. Combining combinations
  9. Probability using permutations and combinations

Probability

Possibility Space (Sample Space)

  1. Possibility space diagrams

Tree Diagrams

  1. Tree Diagrams
  2. Probability Tree Diagrams for Independent Events
  3. And Rule (multiplication) / Or Rule (addition for mutually exclusive events)
  4. Probability Tree Diagrams for Dependent Events
  5. Conditional probability in tree diagrams
  6. Exam Questions - Tree diagrams

Permutations and Combinations in Probability

  1. Probability using permutations and combinations

Discrete Random Variables

Discrete Random Variables

  1. Probability distribution tables
  2. Cumulative distribution function F(X)
  3. Expected values E(X)
  4. Expected values E(X²)
  5. Variance, Var(X)
  6. Linear combinations of discrete random variables
  7. Exam Questions - Discrete random variables

Binomial Distribution

  1. Binomial distribution
  2. Mean and variance
  3. Exam Questions - Binomial distribution

The Normal Distribution

The Normal Distribution

  1. The normal distribution
  2. The standard normal distribution Z~N(0,1) - Using tables or calculator
  3. Probabilities from a normal distribution using tables
  4. Exam Questions - Normal distribution, finding a probability
  5. Calculating the mean μ and standard deviation σ
  6. Exam Questions - Calculating the mean and standard deviation
  7. Exam Questions - Finding an observed value

Normal Approximation to the Binomial Distribution

  1. Continuity corrections
  2. The normal approximation to the binomial distribution
  3. Exam Questions - Normal approximation to the binomial distribution