Making Statistics Vital – Statistics 2 Module
Collection Author: Craig Barton - Maths AST and creator of www.mrbartonmaths.com (TES Name: mrbartonmaths)
What Jonny Griffiths did to enrich the study of Core A Level Mathematics through his phenomenal RISP resources, he was also done here for the study of Statistics with his Making Statistics Vital activities. They have been a godsend for me in my teaching of A Level Stats, giving a rich, challenging and ultimately rewarding option than simply testing students’ understanding through textbook and exam questions.
I will let Mr Griffiths himself give an overview of his excellent collection:
“Welcome to this collection of A Level Statistics tasks; I hope that you will find something here that you would like to try out and that your students will enjoy. There is no explicit overarching philosophy behind the collection - I am not on some crusade to get statistics taught a certain way. I do, however, have the belief that people learn best when they are active, and then reflective, before finally systematising what they have learnt. These tasks also include the idea that we all love to be faced with a puzzle.
Everyone who writes tasks for a maths classroom has a style; what is mine? I would say that although I love teaching statistics, I am a pure mathematician first and a statistician second, and that means that there is definitely a ‘pure maths’ feel to some of these tasks. I have sadly not thus far in my career worked as a professional statistician; I hope that those of you that have will forgive any ‘unworldliness’ in my approach.
All of the activities here have been trialled (and hopefully later improved) in my own classroom. I find that what I need in my S1 and S2 lessons is fairly short activities that are versatile enough to come anywhere in a lesson, and which shed light on a syllabus topic in a fun way that I can later reinforce. The good news is (I hope you will agree with me) that the S1 and S2 modules, certainly with MEI, are not so packed with syllabus material that it becomes hard to justify using tasks like these.
My hope is that in this rag-bag that I present you with here, you will find at least some tasks that you warm to, and which you can customise for your own ends. I would be delighted to learn how you get on with using them.”
This Collection page provides links to all the Making Statistics Vital resources related to the Statistics 2 module.
1. The Poisson distribution
- The idea here is to explore what happens if you add two independent Poisson distributions. Autograph’s statistics abilities will be a big help here. This could be explored by the whole class together on the big screen.
- Here is a spreadsheet that encourages discussion of how a Binomial Distribution can be approximated by a Poisson distribution. Excel is asked to do a lot here, so you have to be a little patient!
- This activity compares a Binomial distribution with its Poisson Approximation. Are there values where the approximation is particularly good? The task requires finding where two almost-identical graphs cross.
2. The Normal Distribution
- This is a close relative of my ‘picking numbers from a bag’ tasks. What happens as you swap the parameters in a Normal question?
- This activity tests at a fairly basic level that students are happy with the mean and variance of the Poisson, Binomial and Normal distributions. A good way to fill a spare fifteen minutes.
- Crossover activities that compare entities that are different but similar are often interesting; here the standard deviation is compared to the inter-quartile range in the context of a Normal Distribution.
3. Sampling and hypothesis testing using the normal distribution
- When it comes to choosing a random sample, is it better to use mechanical methods or intuition?
- Simple Random Sampling requires us to come up with a list of random numbers so that every member of the population has an equal chance of being chosen. Sometimes the way to do this is less obvious than it seems at first glance.
- Students like being given a sheet containing one or two howlers for them to uncover. Here are two problems that make the same error - and its an important one to resolve.
- A filling-the-gaps-type ‘puzzle’ that makes sure students are happy with the mean and variance of the sample mean for a Normal distribution. A certain amount of number theory is required here too to find the unique answer.
4. Contingency Tables and the Chi-Squared Distribution
- By the end of their A2 Statistics course, students will have met a range of different hypothesis tests, all with slightly different ways of structuring things. This activity aims to bring them all together into a single table.
- It is a fact that the chi-squared test can only be carried out using frequencies. This spreadsheet offers a chance to play with the erroneous idea that you can use percentages instead. Probably off your syllabus, but hopefully fun and informative all the same.
5. Bivariate Data, Regression and Correlation
- This activity will probably make purist statisticians scream, but if you are someone like me, you become curious about the qualities that the functions arising in statistics possess, quite independently of considerations of what is sensible statistically.
- Autograph is essential to make this task work. The goal is for students to understand how the regression line is chosen. Autograph has a wonderful built-in facility for showing the squares of the residuals - once seen, never forgotten.
6. Other Resources
- This spreadsheet allows you to investigate raising a 2x2 or 3x3 matrix to a given power. This is extremely useful when the matrix in question is a transition matrix for a Markov Chain. The equilibrium probabilities can clearly be seen here.