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Unit S1: Statistics 1

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  1. S1.1 - Mathematical models in probability and statistics

    1. S1.1.1

      The basic ideas of mathematical modelling as applied in probability and statistics.

  2. S1.2 - Representation and summary of data

    1. S1.2.1Histograms, stem and leaf

      Histograms, stem and leaf Using histograms, stem and leaf diagrams and box plots to diagrams, box plots. compare distributions.; Back-to-back stem and leaf diagrams may be required.; Drawing of histograms, stem and leaf diagrams or box plots will not be the direct focus of examination questions.

    2. S1.2.2Measures of location – mean,

      Measures of location – mean, Calculation of mean, mode and median, range and median, mode. interquartile range will not be the direct focus of examination questions.; Students will be expected to draw simple inferences and give interpretations to measures of location and dispersion.; Significance tests will not be expected.; Data may be discrete, continuous, grouped or ungrouped.; Understanding and use of coding.

    3. S1.2.3Measures of dispersion – variance,

      Measures of dispersion – variance, Simple interpolation may be required.; Interpretation of standard deviation, range and measures of location and dispersion. interpercentile ranges.

    4. S1.2.4Skewness

      Skewness.; Concepts of outliers.; Students may be asked to illustrate the location of outliers on a box plot.; Any rule to identify outliers will be specified in the question.

  3. S1.3 - Probability

    1. S1.3.1Elementary probability

      Elementary probability.

    2. S1.3.2Sample space

      Sample space.; Exclusive and Understanding and use of complementary events.; Conditional P(A′) = 1 − P(A), probability.; P(A ∪ B) = P(A) + P(B) − P(A ∩ B), P(A ∩ B) = P(A) P(B | A).

    3. S1.3.3Independence of two events

      Independence of two events.; P(B | A) = P(B), P(A | B) = P(A), P(A ∩ B) = P(A) P(B).

    4. S1.3.4Sum and product laws

      Sum and product laws.; Use of tree diagrams and Venn diagrams.; Sampling with and without replacement.

  4. S1.4 - Correlation and regression

    1. S1.4.1Scatter diagrams

      Scatter diagrams.; Linear regression.; Calculation of the equation of a linear regression line using the method of least squares.; Students may be required to draw this regression line on a scatter diagram.

    2. S1.4.2Explanatory (independent)

      Explanatory (independent) and Use to make predictions within the range of values of the response (dependent) variables. explanatory variable and the dangers of extrapolation.; Applications and interpretations.; Derivations will not be required.; Variables other than x and y may be used.; Linear change of variable may be required.

    3. S1.4.3Product moment correlation

      The product moment correlation Derivations and tests of significance will not be required. coefficient, its use, interpretation and limitations.

  5. S1.5 - Discrete random variables

    1. S1.5.1concept of a discrete random variable

      The concept of a discrete random variable.

    2. S1.5.2Probability and cumulative distribution functions

      Use the probability function p(x) = P(X = x) and cumulative distribution function F(x0) = P(X ≤ x0) for a discrete random variable.

    3. S1.5.3Mean and variance of a discrete

      Mean and variance of a discrete Use of E(X), E(X 2) for calculating the variance of X. random variable.; Knowledge and use of E(aX + b) = aE(X) + b, Var(aX + b) = a2 Var(X).

    4. S1.5.4discrete uniform distribution

      The discrete uniform distribution.; The mean and variance of this distribution.

  6. S1.6 - The Normal distribution

    1. S1.6.1

      The Normal distribution including Knowledge of the shape and the symmetry of the the mean, variance and use of tables distribution is required.; Knowledge of the probability of the cumulative distribution density function is not required.; Derivation of the mean, function. variance and cumulative distribution function is not required.; Interpolation is not necessary.; Questions may involve the solution of simultaneous equations.