
Description

Outcome

Certification

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

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 numerically
 1.6a 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

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