Chapter

Topic

Number of Weeks

Resources

Comments

1

Mathematical Modelling in probability and statistics

1

Pg’s 1-2

Go over the meaning of quantitative and qualitative data; samples and populations

Pg’s 1-2

Much of the work here can actually be covered in discussion.

2

Graphical representation of sample data (location)

3

Pg 12-28

Frequency distributions; histograms; stem and leaf diagrams, vertical line graphs leading onto cumulative frequency step polygons.

3

Methods for summarising data (dispersion)

5

Pg 29-52

Measures of locations: mode and median.

Measures of spread: quantiles, quartiles (of grouped or discrete data).

Deciles and percentiles.

Calculating quantiles from stem and leaf, cumulative frequency polygons and box and whisker plots.

Coding and weighted means.

4

Methods for summarising data (dispersion)

3

Pg 53 - 68

Explain the terminology

Measures of dispersion:range;IQR;variance

Boxplots and outliers.

Skewness

Test on chapters 1 - 4

5

Probability

3

Pg 69 - 95

Venn diagrams; sample space diagrams; exclusive and complementary events, the addition and multiplication rules.

Conditional probability

Independent events

Tree diagrams

Approximately end of term 1

6

Correlation

2

Pg 114-130

Interpreting the product moment correlation coefficient and calculating it.

7

Regression

2

Pg131-145

Least squares regression line.

Interpretation and extrapolation.

8

Discrete random variables

4

Pg 148 - 166

Probability density function and cumulative density function

Expectation and variance of random variables

Discrete uniform distribution

9

The Normal Distribution

3

Pg 167 - 180

Mean and variance of normal distribution.

Standardising and use of tables

Use of cdf

Approximately end of term 2

Past papers question should be done throughout term 2 and continued after the course has been completed.

Chapter

Topic

Number of Weeks

Resources

Comments

1

Binomial distributions

1

Pg 7-22

Revise factorial notation, pascals triangle and binomials.

Conditions for binomial distribution, probability function, parameters, cumulative probabilities

Mean and variance of the binomial distribution

Poisson distribution

1

Pg 22-36

The mean and variance of the distribution.

Poisson as an approximation to the binomial

Test on chapter 1

2

Continuous Random Variables

2

Pg 37 - 57

Concept of a continuous random variable and its probability density function.

Integration methods may need to be revised

Cumulative distribution function.

Mean and variance of a continuous random variable.

Calculating the mean, median ( Median: F(m) = ½) and quartiles of continuous random variables

Relationship between f(x) and F(x)

Test on chapter 2

3

Continuous distributions

1

Pg 71- 83

Continuous uniform (rectangular) distribution; calculating the mean and variance.

Normal distribution as an approximation to the binomial and poisson distribution.

Using the continuity correction.

4

Hypothesis Tests

3

Pg 85-107

Populations and samples

(Sampling units and frames; advantages and disadvantages); collecting data.

Concept of a statistic.

Hypothesis tests (one and two tailed)

Critical regions

Hypothesis test for the proportion ‘p’ of a binomial and poisson distribution

Test on chapter 4

Aim to finish the course around the end of November

Chapter

Topic

Number of Weeks

Resources

Comments

1

Combinations of Random Variables

0.5

Pg 1 - 6

Finding the expectation and variance of combinations of random variables.

2

Sampling

0.5

Pg 7 - 16

Methods of collecting data

Taking a census and sampling (using random tables).

Other methods of sampling.

Sources of data

(Students find this an easy concept but find the exam questions hard so give plenty of practice).

3

Estimation, confidence intervals and tests

3

Pg 17 - 60

The concept of standard error, estimators and bias.

Distribution of the sample mean.

Sample mean and variance as unbiased estimators of the population parameters. (This is a hard concept so give plenty of examples).

Review the Normal distribution for The Central Limit Theorem.

Confidence intervals/limits.

Hypothesis tests for the mean of a normal distribution with known variance.

Hypothesis tests for the difference between the means of two normal distributions with known variance.

Interpreting results.

Do the review exercise and then a test on chapters 1 to 3

4

Goodness of fit and contingency tables

2

Pg 73 - 104

Forming a hypothesis; finding the goodness of fit and degrees of freedom.

The chi-squares distribution and general methods for testing the goodness of fit when the data are discrete (uniform, binomial, poisson) and continuous.

Contingency tables

5

Regression and correlation

1

Pg 104 - 122

Spearmans Rank correlation coefficient.

Testing the hypothesis that a correlation coefficient/population rank is zero

Do the review exercise and then a test on chapters 4 and 5

Remainder of term

Past papers

Students can be given weekly test on the S2 and S3 syllabus. The Delphis tests can be used for this.