Leaving Certificate - Probability and Statistics Ordinary Level

This course covers Probability and Statistics for the Irish Leaving Certificate maths curriculum.

Probability and Statistics
Free Course
This course covers Probability and Statistics for the Irish Leaving Certificate maths curriculum.
  • Duration

    2-3 Hours
  • Assessment

  • Certification

  • Publisher






View course modules


Probability and Statistics is one of two strands introduced in the first phase of the new Project Maths Course. This topic covers up to half of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum.

Statistics are used in real life to make sense of the information around us and how it affects us. Statistics looks at the data handling cycle and analysis of the data collected. This involves posing a question, collecting data on that question, presenting that data, analysing the data (using measures of spread and centre) and interpreting the results. In answering questions, it is essential that you can contextualise and justify your findings.

Probability is concerned with the likelihood of an event(s) happening. The information can be used to make informed decisions. The use of probability is commonly utilised in the world of finance, insurance and sport among others. Probability can also be used to infer the fairness of an event or series of events. It can be evaluated using a diagram or a rule-based approach.

This Strand attempts to merge the mathematical aspects of Probability and Statistics with its real-life application. It is an interesting topic that is very accessible to all students.

Start Course Now


Module 13: Probability

Module 10: Measures of Central Tendency

Module 11: Measures of Central Spread

Module 14: Expected Value

Module 15: Binomial Distributions and Bernoulli Trials

Module 16: Normal Distribution

Module 17: The Data Handling Cycle

Module 1: Types of Data and Sampling

Module 2: Frequency Tables

Module 3: Methods of Representing Data

Module 4: Pie Charts

Module 6: Stem-and-Leaf Plots

Module 5: Histograms and Bar Charts

Module 7: Skewness

Module 8: Scatter Plots - Line of Best Fit

Module 9: Correlation

Module 12: Analyse Data

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 back-to-back 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 inter-quartile 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 problem-solving 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


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 official Certification, which is a great way to share your achievement with the world. Your Alison Certification 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 Certification 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 security-marked Certificate, posted to you with FREE shipping
Framed Certificate - a physical version of your officially branded and security-marked Certificate in a stylish frame, posted to you with FREE shipping

All Certification is available to purchase through the Alison Shop. For more information on purchasing Alison Certification, please visit our faqs. If you decide not to purchase your Alison Certification, 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 Certification pricing, please visit our Pricing Page.



    You have received a new notification

    Click here to view them all