Leaving Certificate - Probability and Statistics Ordinary Level

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.

Probability and Statistics
Free Course
This free online ordinary level probability and statistics course teaches you what you need to know to pass your leaving certificate exam. You will study the data handling cycle and the analysis of the collected data, the fundamental principle of counting, and the basic rules of probability. This course will also discuss permutations and combinations as well as teach you how to use a frequency table, pie chart, bar chart, histogram, and more!
  • Duration

    1.5-3 Hours
  • Certification

  • Publisher

  • Accreditation






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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 rule-based 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!

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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


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