Applications and Interpretation SL
- Concepts of population, sample, random sample, discrete and continuous data
- Reliability of data sources and bias in sampling
- Interpretation of outliers
- Sampling techniques and their effectiveness
- Presentation of data (discrete and continuous): frequency distributions (tables)
- Histograms
- Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR)
- Production and understanding of box and whisker diagrams
- Measures of central tendency (mean, median and mode)
- Estimation of mean from grouped data
- Model class
- Measures of dispersion (interquartile range, standard deviation and variance)
- Effect of constant changes on the original data
- Quartiles of discrete data
- Linear correlation of bivariate data
- Pearson’s product-moment correlation coefficient, r
- Scatter diagrams; lines of best fit, by eye, passing through the mean point
- Equation of the regression line of y on x
- Use of the equation of the regression line for prediction purposes
- Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b
- Concepts of trial, outcome, equally likely outcomes, relative frequency, sample space (U) and event
- The probability of an event A is P(A) = n(A) / n(U)
- The complementary events A and A′ (not A)
- Expected number of occurrences
- Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities
- Combined events and mutually exclusive events
- Conditional probability
- Independent events
- Concept of discrete random variables and their probability distributions
- Expected value (mean), E(X) for discrete data
- Binomial distribution
- Mean and variance of the binomial distribution
- The normal distribution and curve
- Properties of the normal distribution
- Diagrammatic representation
- Normal probability calculations
- Inverse normal calculations
- Spearman’s rank correlation coefficient, rs
- Awareness of the appropriateness and limitations of Pearson’s product moment correlation coefficient and Spearman’s rank correlation coefficient, and the effect of outliers on each
- Formulation of null and alternative hypotheses, H0 and H1
- Significance levels
- p -values
- Expected and observed frequencies
- The χ2 test for independence: contingency tables, degrees of freedom, critical value
- The χ2 goodness of fit test
- The t -test
- Use of the p -value to compare the means of two populations
- Using one-tailed and two-tailed tests
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Analysis and Approaches SL
- Concepts of population, sample, random sample, discrete and continuous data
- Reliability of data sources and bias in sampling
- Interpretation of outliers
- Sampling techniques and their effectiveness
- Presentation of data (discrete and continuous): frequency distributions (tables)
- Histograms
- Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR)
- Production and understanding of box and whisker diagrams
- Measures of central tendency (mean, median and mode)
- Estimation of mean from grouped data
- Model class
- Measures of dispersion (interquartile range, standard deviation and variance)
- Effect of constant changes on the original data
- Quartiles of discrete data
- Linear correlation of bivariate data
- Pearson’s product-moment correlation coefficient, r
- Scatter diagrams; lines of best fit, by eye, passing through the mean point
- Equation of the regression line of y on x
- Use of the equation of the regression line for prediction purposes
- Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b
- Concepts of trial, outcome, equally likely outcomes, relative frequency, sample space (U) and event
- The probability of an event A is P(A) = n(A) / n(U)
- The complementary events A and A′ (not A)
- Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities
- Combined events and mutually exclusive events
- Conditional probability
- Independent events
- Concept of discrete random variables and their probability distributions
- Expected value (mean), for discrete data
- Applications
- Binomial distribution
- Mean and variance of the binomial distribution
- The normal distribution and curve
- Properties of the normal distribution
- Diagrammatic representation
- Normal probability calculations
- Inverse normal calculations
- Equation of the regression line of x on y
- Use of the equation for prediction purposes
- Use of the probability formulae for conditional and independent events
- Standardization of normal variables (z– values)
- Inverse normal calculations where mean and standard deviation are unknown
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