International Baccalaureate Mathematics Analysis and Approaches
Statistics and Probability
These are the statements describing what students need to learn:
[Higher Level only statements are in blue]
- 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. Modal 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: P(A∪B)=P(A)+P(B)-P(A∩B). Mutually exclusive events: P(A∩B)=0. Conditional probability: P(A|B)=P(A∩B)/P(B). Independent events: P(A∩B)=P(A)P(B)
- 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
- formal definition and use of the formulae: P(A|B)=P(A∩B)/P(B) for conditional probabilities, and P(A|B)=P(A)=P(A|B') for independent events
- standardization of normal variables (z- values). Inverse normal calculations where mean and standard deviation are unknown
- Use of Bayes’ theorem for a maximum of three events.
- Variance of a discrete random variable.
Continuous random variables and their probability density functions.
Mode and median of continuous random variables.
Mean, variance and standard deviation of both discrete and continuous random variables.
The effect of linear transformations of X.
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