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19
Modules
101
Topics
1.53
hours
Modules (19)
Resources ()

leaving certificate  statistics higher level

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Module 1
Types of Data and Sampling
Resources availableThe aim of statistics is to help us make sense of large amounts of information and figure out what it means and how it affects us. Data must be gathered from samples and analysed and it is often the case that this data is either number based or word based. This gives rise to different types of data and samples. Terminology is very important in this topic.Introduction to data
Start TopicOverview of data
Start TopicTypes of data
Start TopicCategorical data
Start TopicNumerical data
Start TopicContinuous and discrete data
Start TopicSample types
Start Topic 
Module 2
Frequency Tables
Resources availableFrequency tables help make the analysis of collected data much easier as they group the data into categories. They enable the mean, mode and median to be calculated more clearly.Frequency and graphs  Overview
Start TopicFrequency tables with nominal data
Start TopicFrequency tables with discrete data
Start TopicFrequency tables  Discrete data and summary statistics
Start TopicMean from frequency tables  Discrete data
Start TopicInterpreting bar graphs
Start Topic 
Module 3
Methods of Representing Data
Resources availableData can be presented in many pictorial forms. The graph used will vary depending on the data being presented.Representing data
Start TopicLine graphs
Start TopicLine plots
Start Topic 
Module 4
Pie Charts
Resources availablePie charts are used to display discrete numerical data or categorical data.Pie charts
Start TopicPie charts  Worked example
Start Topic 
Module 5
Histograms and Bar Charts
Resources availableHistograms and Bar Charts are very similar but there are some important differences  no gaps between bars in histograms, bar charts show discrete data but histograms show continuous data and data is always grouped in histograms.Histograms & bar graphs
Start TopicBar graphs
Start Topic 
Module 6
StemandLeaf Plots
Resources availableStem & Leaf diagrams are similar to horizontal Bar Charts but are only suitable for small amounts of data. It is important that a Key is always included to explain the data presented.Introduction to stemandleaf
Start TopicStemandleaf plots
Start TopicBack to back stem plots
Start TopicStemandleaf diagrams 1
Start TopicStemandleaf diagrams 2
Start Topic 
Module 7
Skewness
Resources availableIt is possible to determine the distribution of data by looking at the shape of the histogram. There are 3 main shapes – symmetrical, positive/right and negative/left skewness.Comparing mean, mode and median
Start TopicSymmetry and skew of a distribution
Start TopicNegative skewness – Left skewness
Start TopicPositive skewness – Right skewness
Start TopicProbability intervals
Start TopicComparing sample and population
Start TopicProbability intervals  Examples
Start Topic 
Module 8
Scatter Plots  Line of Best Fit
Resources availableScatter Plots are graphs that display and compare bivariate data (2 variables). Look for a relationship between the two variables and comment on the strength of the relationship. Using information on the graph, we can find the equation of a line that best describes this relationship.Scatterplots
Start TopicStrength of association
Start TopicIntroduction to the regression line
Start TopicFinding the equation of a regression line
Start TopicIntrepretation of slope and intercept
Start TopicPractice question
Start TopicScatter plots and linear models
Start Topic 
Module 9
Correlation
Resources availableCorrelation is a measure of the strength of a relationship between bivariate data. Correlation can be classified as positive, negative or no correlation (0) and it is always a value between 1 and 1.Correlation coefficient: r
Start TopicCalculating r
Start TopicPractice question
Start TopicCorrelation and causation
Start Topic 
Module 10
Measures of Central Tendency
Resources availableAnalysing a large mass of data can be easily summarised using some key numbers – mean, mode and median. It is important that you can identify/calculate these values. Also, at times certain values may be more appropriate than others to use; therefore you must be able to justify your choice based on the information to hand.Measures of central tendency: Mean, mode and median
Start TopicMode
Start TopicMean
Start TopicMedian
Start TopicMode, mean and median
Start TopicComparing mode, mean and median
Start Topic 
Module 11
Measures of Central Spread
Resources availableMeasures of spread reflect the range over which the data is varied or spread out. The data ranges across four different quartiles which give the interquartile range. Standard deviation is a very important measure of spread that shows how far the data is spread from the mean. Outliers are extreme values that will affect analysis of any dataset.Measures of central spread
Start TopicRange of data
Start TopicInterquartile range
Start TopicStandard deviation as a measure of spread
Start TopicSummarising data  Overview
Start TopicSoccer activity
Start Topic 
Module 12
Analyse Data
Resources availableHaving collected and presented data, conclusions must be drawn. Measure of Central Tendency and Spread must be used.Mean from frequency tables  Discrete data
Start TopicFrequency and graphs  Overview
Start TopicSummarising data  Overview
Start TopicMode
Start TopicMean
Start TopicMedian
Start TopicMode, mean, median
Start TopicComparing mode, mean and median
Start TopicRange of data
Start TopicInterquartile range
Start TopicReview  Summarising data
Start TopicStandard deviation and normal distribution
Start TopicStandard deviation and calculator
Start Topic 
leaving certificate  probability higher level

Module 13
Probability
Resources availableProbability is concerned with the ‘chance’ that something may happen. Probability of events occurring may be calculated using rules or diagrams (tables/tree/Venn diagrams). Particular attention should also be paid to the terminology of this topic.Fundamental Principle of Counting
Start TopicCalculating the outcome
Start TopicPermutations and combinations
Start TopicIntroduction to probability
Start TopicProbabilities
Start TopicFinding probabilities theoretically
Start TopicBasic rules of probability
Start TopicVenn diagrams
Start TopicConditional probability
Start Topic 
Module 14
Expected Value
Resources availableExpected value is used widely in insurance industries and casino games to determine the fairness of the result/payout. We can use this value to determine the potential loss/gain of an event for us. Expected value of 0 means a game is fair/equitable. The expected value does not have to be one of the possible outcomes of the event.Probability and relative frequency
Start TopicShortrun coin tossing
Start TopicShortrun dice rolling
Start TopicPredicting from past experience
Start TopicTowards probability with coins
Start TopicTowards probability with dice
Start TopicProbability as longrun relative frequency
Start TopicMean and variance of a discrete random variable
Start Topic 
Module 15
Binomial Distribution
Resources availableBinomial distribution is a method of calculating probabilities that can only be applied in certain circumstances – Bernoulli trials. If the situation FITS it must be Bernoulli! Fixed number of trials; independent events; two possible outcomes; success/failure probability remains constant.Binomial probability function and distribution
Start TopicThe number of successes in a given number of trials
Start TopicBinomial distribution: Bernoulli trials
Start TopicBernoulli extended
Start Topic 
Module 16
Normal Distribution
Resources availableWhen data is arranged in order from lowest to highest, a pattern may emerge where the majority of the data may form a cluster around the middle. Graphing this information would produce a bellshaped curve known as the normal distribution curve. 3 values are important when dealing with the normal curve – 68%, 95% and 99.7%. Wide, flatter curves suggest greater spread/std. deviation, whereas narrow, steeper curves suggest smaller spread between values/std. deviations. Standard scores/zscores are the number of std. deviations a values lies above or below the mean.Introduction to the normal distribution
Start TopicThe normal curve
Start TopicContinuous random variables and the normal distribution
Start TopicCalculation of probabilities for a normal distribution
Start Topic 
Module 17
Hypothesis Testing
Resources availableA hypothesis is a statement made about some characteristic of a population and hypothesis testing is a statistical method of proving/disproving it. The truth of the statement depends on if the statistic lies within a calculated confidenceinterval level.Hypothesis testing
Start TopicHypothesis testing  Example
Start TopicHypothesis testing  Formal Procedure
Start TopicWorked example
Start Topic 
Module 18
Problem Solving
Resources availableAn example putting what we have learned so far into practice.Random variables
Start TopicProbability of events
Start TopicStandard deviation as a measure of spread
Start Topic 
end of course information

End of Course Information
Resources availableInformation about Certificate of Completion.End of course information
Start Topic