Leaving Certificate  Probability and Statistics Higher Level
Learn to make informed decisions with this Probability and Statistics for the Irish Leaving Certificate course.
Description
This course begins with an introduction to data. You will study the different types of data including categorical data, numerical data, and continuous and discrete data. You will also look into the frequency table, pie chart, histogram, and bar chart. This course will also discuss the methods of representing data, the measures of central tendency and central spread, stemandleaf plots, skewness, and correlation as well as the mean, median, mode, range, and interquartile range.
You will then look into probability which is concerned with the chance that something may happen. You will learn how to calculate for the probability of events occurring using rules or diagrams such as tables, tree, and Venn diagrams. You will learn about the expected value which is used widely in insurance industries and casino games, study binomial and normal distribution, hypothesis testing which is a statistical method of proving/disproving a hypothesis, and more.
Probability is concerned with the likelihood of an event happening and a combination of probability and statistics can be used to prove/disprove a given conjecture or statement. Upon the completion of this course, you will gain better insight into the mathematical aspects of probability and statistics with reallife applications to help you make informed decisions. Sign up for this course and gain a better understanding of Probability and Statistics today!
Modules
Module 13: Probability

Fundamental Principle of Counting

Calculating the outcome

Permutations and combinations

Introduction to probability

Probabilities

Finding probabilities theoretically

Basic rules of probability

Venn diagrams

Conditional probability
Module 15: Binomial Distribution

Binomial probability function and distribution

The number of successes in a given number of trials

Binomial distribution: Bernoulli trials

Bernoulli extended
Module 16: Normal Distribution

Introduction to the normal distribution

The normal curve

Continuous random variables and the normal distribution

Calculation of probabilities for a normal distribution
Module 17: Hypothesis Testing

Hypothesis testing

Hypothesis testing  Example

Hypothesis testing  Formal Procedure

Worked example
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 3: Methods of Representing Data
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 8: Scatter Plots  Line of Best Fit

Scatterplots

Strength of association

Introduction to the regression line

Finding the equation of a regression line

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 4: Pie Charts
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 as a measure of spread

Summarising data  Overview

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

Mean and variance of a discrete random variable
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 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 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
  count the number of ways of selecting 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
  extend their understanding of the basic rules of probability (AND/OR, mutually exclusive) through the use of formulae
  use the Addition Rule, Multiplication Rule (Independent events), Multiplication Rule (General case)
  solve problems involving conditional probability in a systematic way
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
  solve problems involving calculating the probability of k successes in n repeated Bernoulli trials (normal approximation not required)
  calculate the probability that the kth success occurs on the nth Bernoulli trial
  use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions
  solve problems involving reading probabilities from the normal distribution tables
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
  recognise the importance of randomisation and the role of the control group in studies
  recognise biases, limitations and ethical issues of each type of study
  select a sample (stratified, cluster, quota – no formulae required, just definitions of these)
  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
  analyse plots of the data to explain differences in measures of centre and spread
  draw the line of best fit by eye
  make predictions based on the line of best fit
  calculate the correlation coefficient by calculator
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
  recognise the effect of outliers
  use percentiles to assign relative standing
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
  recognise the concept of a hypothesis test
  calculate the margin of error for a population proportion
  conduct a hypothesis test on a population proportion using the margin of error
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:
Ideal for sharing with potential employers  include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Certificates for completed Certificate courses:
Digital Certificate  a downloadable Certificate in PDF format, immediately available to you when you complete your purchase
Certificate  a physical version of your officially branded and securitymarked Certificate, posted to you with FREE shipping
Framed Certificate  a physical version of your officially branded and securitymarked Certificate in a stylish frame, posted to you with FREE shipping
All Certificates are available to purchase through the Alison Shop. For more information on purchasing Alison Certificates, please visit our FAQs. If you decide not to purchase your Alison Certificate, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Certificate pricing, please visit our Pricing Page.
Careers
This Course has been revised!
For a more enjoyable learning experience, we recommend that you study the mobilefriendly republished version of this course.
Take me to revised course.