Leaving Certificate - Probability and Statistics Higher Level

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Leaving Certificate - Probability and Statistics Higher Level

Learn to make informed decisions with this Probability and Statistics for the Irish Leaving Certificate course.

Probability and Statistics
Free Course
This free online leaving certificate maths course will teach you about ordinary level probability and statistics. In this course you will learn about the data handling cycle and analyse data collected by posing a question, as well as how to collect data on a question, present data, analyse data using measures of spread and centre, interpret results, and a whole lot more. This course will get you ready for your leaving cert maths exam fast.
  • Duration

    1.5-3 Hours
  • Certification

  • Publisher

  • Accreditation






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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, stem-and-leaf 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 real-life applications to help you make informed decisions. Sign up for this course and gain a better understanding of Probability and Statistics today!

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Module 13: Probability

Module 15: Binomial Distribution

Module 16: Normal Distribution

Module 17: Hypothesis Testing

Module 1: Types of Data and Sampling

Module 3: Methods of Representing Data

Module 6: Stem-and-Leaf Plots

Module 5: Histograms and Bar Charts

Module 8: Scatter Plots - Line of Best Fit

Module 9: Correlation

Module 12: Analyse Data

Module 4: Pie Charts

Module 10: Measures of Central Tendency

Module 11: Measures of Central Spread

Module 14: Expected Value

Module 2: Frequency Tables

Module 7: Skewness

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 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
  • - 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 inter-quartile 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 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


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