
Description

Outcome

Certification

Probability and Statistics is one of two strands introduced in the first phase of the new Project Maths Course in the Irish curriculum. This topic covers up to half of the new Paper 2 in the Leaving Certificate Paper.
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. A combination of Probability and Statistics can be used to prove/disprove a given conjecture or statement (Hypothesis Testing (HL only)).
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
  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 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
  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

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