**Mathematical Models in Probability and Statistics**

The basic ideas of mathematical modelling applied to probabilty and statistics

**Representation and Summary of Data**

Histograms

Stem and leaf diagrams

Box plots

Measures of location - mean, median and mode

Coding

Discrete, continuous, grouped and ungrouped data

Measures of dispersion - variance, standard deviation, range, interpercentile ranges

Interpolation

Skewness

Outliers

**Probability**

Elementary probability

Sample space

Exclusive and complementary events

Conditional probability

Independence of two events

Sum and product laws

Tree diagrams

Venn diagrams

**Correlation and Regression**

Scatter diagrams

Linear regression

Method of least squares

Explanatory (independent) and response (dependent) variables

The use, interpretation and limitations of the product moment correlation coefficient

**Discrete Random Variables**

The concept of a discrete random variable

The probabilty function for a discrete random variable

The cumulative distribution function for a discrete random variable

Mean and variance of a discrete random variable

The discrete unform distribution

**The Normal Distribution**

The Normal distribution including the mean, variance and the use of the tables for the cumulative ditribution function