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16 units · 57 lessons

Probability and Statistics

Probability and Statistics from the first idea to exam level: every lesson builds on the one before, with a worked example, a step-through diagram where it helps, a quick check and practice that adapts to what you know. Follows Walpole, Myers, Myers & Ye, Probability & Statistics for Engineers & Scientists, 9th ed. (with Bluman, Elementary Statistics).

Probability and Statistics at a glance

What does Probability and Statistics cover?

Describing Data, Central Tendency, Dispersion & Position, Counting, Probability Rules, Conditional Probability & Bayes, Random Variables, Discrete Distributions, Continuous Distributions, Normal Distribution, Sampling Distributions, Estimation, Hypothesis Testing and Correlation & Regression. It follows Walpole, Myers, Myers & Ye, Probability & Statistics for Engineers & Scientists, 9th ed. (with Bluman, Elementary Statistics).

How many lessons does the Probability and Statistics course on Studious have?

16 units and 57 lessons, from "What statistics is" to "The coefficient of determination and prediction". Each lesson has a worked example, a quick check and practice that adapts to what you know, and many have step-by-step diagrams.

Course outline

  1. Unit 1 · Week 1

    Data and Statistics

    1. What statistics is
    2. Types of data and scales of measurement
    3. Collecting data: sampling methods and bias
  2. Unit 2 · Week 2

    Organising and Graphing Data

    1. Frequency distributions
    2. Histograms, frequency polygons and ogives
    3. Bar charts, pie charts and stem-and-leaf plots
  3. Unit 3 · Week 3

    Measures of Central Tendency

    1. The mean
    2. The median and the mode
    3. Mean, median and mode for grouped data
    4. Choosing a measure: shape and skew
  4. Unit 4 · Week 4

    Measures of Dispersion

    1. Range, variance and standard deviation
    2. Variance and standard deviation for grouped data
    3. Coefficient of variation
  5. Unit 5 · Week 5

    Measures of Position

    1. Quartiles, percentiles and the interquartile range
    2. Box plots and outliers
    3. z-scores, the empirical rule and Chebyshev's theorem
  6. Unit 6 · Week 6

    Counting Techniques

    1. The multiplication rule and tree diagrams
    2. Permutations
    3. Combinations
  7. Unit 7 · Week 7

    Basics of Probability

    1. Experiments, sample spaces and events
    2. Classical, empirical and subjective probability; the axioms
    3. The addition rule and complements
    4. Probability with counting
  8. Unit 8 · Week 8

    Conditional Probability and Bayes' Theorem

    1. Conditional probability and the multiplication rule
    2. Independent events
    3. The law of total probability
    4. Bayes' theorem
  9. Unit 9 · Week 9

    Random Variables

    1. Discrete random variables and probability mass functions
    2. Cumulative distribution functions
    3. Expected value
    4. Variance of a random variable, and E(aX + b)
  10. Unit 10 · Week 10

    Discrete Probability Distributions

    1. Bernoulli trials and the binomial distribution
    2. Mean and variance of the binomial
    3. The Poisson distribution
    4. Geometric and hypergeometric distributions
  11. Unit 11 · Week 11

    Continuous Random Variables

    1. Probability density functions: probability as area
    2. The uniform distribution
    3. The exponential distribution
  12. Unit 12 · Week 12

    The Normal Distribution

    1. The normal curve and its properties
    2. The standard normal distribution and z-tables
    3. Applications: finding probabilities and cut-off values
    4. Normal approximation to the binomial
  13. Unit 13 · Week 13

    Sampling Distributions

    1. Sampling distribution of the sample mean
    2. The central limit theorem
    3. Sampling distribution of a proportion
  14. Unit 14 · Week 14

    Estimation

    1. Point estimates and standard error
    2. Confidence interval for a mean (σ known)
    3. Confidence interval with the t distribution
    4. Confidence interval for a proportion, and sample size
  15. Unit 15 · Week 15

    Hypothesis Testing

    1. Null and alternative hypotheses, Type I and Type II errors
    2. The z-test for a mean and p-values
    3. The t-test for a mean
    4. Testing a proportion
    5. The chi-square test of independence
  16. Unit 16 · Week 16

    Correlation and Regression

    1. Scatter plots and the correlation coefficient
    2. The least-squares regression line
    3. The coefficient of determination and prediction

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