Leaving Certificate  Probability and Statistics Ordinary Level
Learn how to use probability to find the likelihood of an event(s) happening as well as analyse data using statistics.
Description
This course begins with an introduction to data. You will learn that univariate data is data involving one variable and bivariate data involves two pieces of data. You will also look into categorical data, numerical data, and continuous and discrete data as well as sample types including simple random, stratified, cluster, quota, and convenience sampling. You will also look study the frequency table, pie chart, stem and leaf plot, histogram and bar chart.
You will then study the fundamental principle of counting which states that If there are m ways for one activity to occur, and n ways for a second activity to occur, then there are m*n ways for both to occur. This course will also discuss permutations and combinations. You will look into probability which is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes. You will also learn how to find probabilities theoretically, study the basic rules of probability, and more.
The use of probability is commonly utilised in the world of finance, insurance, and sport and can also be used to infer the fairness of an event or series of events while statistics are used in real life to make sense of the information around us and how it affects us. Upon the completion of this course, you will be able to evaluate a probability using a diagram or a rulebased approach as well as use statistics to look at the data handling cycle and analyse data collected. Sign up for this course and start learning today!
Modules
Module 13: Probability

Listing outcomes

Fundamental Principle of Counting

Calculating the outcome

Permutations and combinations

Introduction to probability

Probabilities

Finding probabilities theoretically

Basic rules of probability

Venn diagrams
Module 10: Measures of Central Tendency

Measures of central tendency: Mean, mode and median

Mode

Mean

Median

Mode, mean and median

Comparing mode, mean and median
Module 11: Measures of Central Spread

Measures of central spread

Range of data

Interquartile range

Standard deviation

Summarising data

Soccer activity
Module 14: Expected Value

Probability and relative frequency

Shortrun coin tossing

Shortrun dice rolling

Predicting from past experience

Towards probability with coins

Towards probability with dice

Probability as longrun relative frequency

Expected value  Example
Module 15: Binomial Distributions and Bernoulli Trials
Module 16: Normal Distribution
Module 17: The Data Handling Cycle
Module 1: Types of Data and Sampling

Introduction to data

Overview of data

Types of data

Categorical data

Numerical data

Continuous and discrete data

Sample types
Module 2: Frequency Tables

Frequency and graphs  Overview

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  Discrete data and summary statistics

Mean from frequency tables  Discrete data

Interpreting bar graphs
Module 3: Methods of Representing Data
Module 4: Pie Charts
Module 6: StemandLeaf Plots

Introduction to stemandleaf

Stemandleaf plots

Back to back stem plots

Stemandleaf diagrams 1

Stemandleaf diagrams 2
Module 5: Histograms and Bar Charts
Module 7: Skewness

Comparing mean, mode and median

Symmetry and skew of a distribution

Negative skewness – Left skewness

Positive skewness – Right skewness

Probability intervals

Comparing sample and population

Probability intervals  Examples
Module 8: Scatter Plots  Line of Best Fit

Scatterplots

Strength of association

Intrepretation of slope and intercept

Practice question

Scatter plots and linear models
Module 9: Correlation
Module 12: Analyse Data

Mean from frequency tables  Discrete data

Frequency and graphs  Overview

Summarising data  Overview

Mode

Mean

Median

Mode, mean, median

Comparing mode, mean and median

Range of data

Interquartile range

Review  Summarising data

Standard deviation and normal distribution

Standard deviation and calculator
Module 18: Problem Solving
End of Course Information
Learning Outcomes
Students will learn about:1.1 Counting
  count the arrangements of n distinct objects (n!)
  count the number of ways of arranging r objects from n distinct objects
1.2 Concepts of probability
  discuss basic rules of probability (AND/OR, mutually exclusive) through the use of Venn diagrams
  calculate expected value and understand that this does not need to be one of the outcomes
  recognise the role of expected value in decision making and explore the issue of fair games
1.3 Outcomes of random processes
  find the probability that two independent events both occur
  apply an understanding of Bernoulli trials
  solve problems involving up to 3 Bernoulli trials
  calculate the probability that the 1st success occurs on the nth Bernoulli trial where n is specified
1.4 Statistical reasoning with an aim to becoming a statistically aware consumer
  work with different types of bivariate data
1.5 Finding, collecting and organising data
  discuss different types of studies: sample surveys, observational studies and designed experiments
  design a plan and collect data on the basis of above knowledge
1.6 Representing data graphically and numerically1.6a Graphical
  describe the sample (both univariate and bivariate data) by selecting appropriate graphical or numerical methods
  explore the distribution of data, including concepts of symmetry and skewness
  compare data sets using appropriate displays, including backtoback stem and leaf plots
  determine the relationship between variables using scatterplots
  recognise that correlation is a value from 1 to +1 and that it measures the extent of the linear relationship between two variables
  match correlation coefficient values to appropriate scatter plots
  understand that correlation does not imply causality
1.6b Numerical
  recognise standard deviation and interquartile range as measures of variability
  use a calculator to calculate standard deviation
  find quartiles and the interquartile range
  use the interquartile range appropriately when analysing data
  recognise the existence of outliers
1.7 Analysing, interpreting and drawing inferences from data
  interpret a histogram in terms of distribution of data
  make decisions based on the empirical rule
1.8 Synthesis and problemsolving skills
  explore patterns and formulate conjectures
  explain findings
  justify conclusions
  communicate mathematics verbally and in written form
  apply their knowledge and skills to solve problems in familiar and unfamiliar contexts
  analyse information presented verbally and translate it into mathematical form
  devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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