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# 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.

2-3 Hours

Yes

Yes

XSIQ

## Description

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.

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## Learning Outcomes

• - 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

## Certification

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:

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