Unit S1: Statistics 1

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

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.

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.

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

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.

Elementary probability.

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).

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

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

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.

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.

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

The concept of a discrete random variable.

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

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).

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

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.