SL 4.1

• • 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.

SL 4.2

• • 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.

SL 4.3

• • 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.

SL 4.4

• • 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

SL 4.5

• • 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.

SL 4.6

• • 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).

 SL 4.7

• • Concept of discrete random variables and their probability distributions.

  • Expected value (mean), for discrete data.

  • Applications.

SL 4.8

• • Binomial distribution.

  • Mean and variance of the binomial distribution.

SL 4.9

• • The normal distribution and curve.

  • Properties of the normal distribution.

  • Diagrammatic representation.

  • Normal probability calculations.

  • Inverse normal calculations

SL 4.10

• • Equation of the regression line of x on y.

  • Use of the equation for prediction purposes

SL 4.11

• • Formal definition and use of the formulae:

    • • • • P(A|B) = P(A ∩ B) / P(B) for conditional probabilities,

          • P(A|B) = P(A) = P(A|B′) for independent events.

SL 4.12

• • Standardization of normal variables (z- values).

  • Inverse normal calculations where mean and standard deviation are unknown.

AHL 4.13

• • Use of Bayes’ theorem for a maximum of three events.

AHL 4.14

• • 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