What | Professional Learning for FMU2 (Further Statistics) |

Who | KS5 teachers |

When | September to December 2022 |

How | online |

To book | b.h.denyer@swansea.ac.uk |

**More information**

The course will be run in four hybrid sessions:

All sessions are from 6.30pm to 8pm unless otherwise stated.

FM Unit 2 | Introduction | Drop-in | Final |

Session 1 | Wed Oct 5th | Thurs Oct 13th | Thurs Oct 20th |

Session 2 | Tues Oct 25th | Mon Nov 7^{th} (7-8pm) | Wed Nov 9^{th} |

Session 3 | Tues Nov 15^{th} | Thurs Nov 24^{th} (7- 8.30) | Wed Nov 30^{th} |

Session 4 | Tues Dec 6th | Thurs Dec 15^{th} (7- 8.30) | Wed Jan 11^{th} 2023 |

(i)**Discrete probability distributions:**

Find the mean and variance of simple discrete probability distributions and expectation algebra with discrete ( and continuous random variables) probability distributions.

(ii)**Continuous probability distributions:**

Understand and use probability density and cumulative distribution functions and their relationships. Find and use the median, quartiles and percentiles, mean, variance and standard deviation. Understand and use the expected value of a function of a continuous random variable.

**Poisson and exponential distributions:**

Find and use the mean and variance of a Poisson distribution and an exponential distribution. Understand and use Poisson as an approximation to the binomial distribution. Apply the result that the sum of independent Poisson random variables has a Poisson distribution. Use of the exponential distribution as a model for intervals between events.

(iii)**Understand and use correlation and linear regression**:

Explore the relationships between several variables. Calculate and interpret both Spearman’s rank correlation coefficient and Pearson’s product-moment correlation coefficient.

Calculate and interpret the coefficients for a least squares regression line in context; interpolation and extrapolation.

(iv)**Understand and use the Chi-squared distribution:**

Conduct goodness of fit test, use χ^{2} as an approximate statistic. Use χ^{2} test to test for association in a contingency table and interpret results.

Each session of work will last 2-3 weeks.

Each session will start with an introductory Zoom session, where you will received a recourse pack of study materials containing

- explanatory powerpoints with exercises and answers
- where appropriate, supporting geogebra or excel resources
- an additional powerpoint containing a selection of exam style questions (without solutions).

During the session you will have email access to the tutor and we hope to arrange a voluntary “drop-in” zoom meeting where you can discuss the content with other colleagues and/or the tutor.

At the end of the session there will be zoom meeting which, it is hoped, everyone will be able to attend. During this session, solutions to the powerpoint of exam style questions will be considered and there will be opportunities to discuss any difficulties that have occurred.