Topic 5 – Core: Statistics and probability

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. How to interpret class intervals
  4. Exam Questions - Estimating the median from a grouped frequency table
  5. Exam Questions - Estimating the median from a histogram

Standard Deviation

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

Statistical Diagrams

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

Probability

Possibility Space (Sample Space)

  1. Possibility space diagrams

Tree Diagrams

  1. Exam Questions - Tree diagrams

Venn Diagrams

  1. Exam Questions - Venn diagrams

Independent, Dependent and Mutually Exclusive Events

    Discrete Random Variables

    Discrete Random Variables

    1. Expected values E(X)
    2. Variance, Var(X)
    3. Linear combinations of discrete random variables
    4. Exam Questions - Discrete random variables

    Binomial Distribution

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

    Poisson Distribution

    1. Poisson distribution
    2. Changing the mean
    3. Exam Questions - Poisson distribution

    The Normal Distribution

    The Normal Distribution

    1. The standard normal distribution Z~N(0,1) - Using tables or calculator
    2. Probabilities from a normal distribution using tables
    3. Exam Questions - Normal distribution, finding a probability
    4. Sampling distribution of the sample means (Normal distribution)
    5. Sampling distribution of the sample means (Normal distribution) proof
    6. Introduction to Hypothesis testing for Normal distribution
    7. Hypothesis testing for Normal distribution (One tailed and 2 tailed test)
    8. Understanding Critical values (Hypothesis testing for Normal Distribution)
    9. Hypothesis testing for Normal Distribution - Critical values method (3 examples)