# Making Statistics Vital – Statistics 1 Module

#### TES Secondary maths resource collections

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 1 module.

#### 1.Data Presentation

MSV 1: Histogram Cut-up

• This activity attempts to get students to think about frequency density and how it is used in the construction of a histogram. The is a distinctly ‘puzzle’ feel to this task, which can take a good half-hour working in pairs.

#### 2. Measures of Centre and Spread

MSV 4: Outlier Tester

• This is a really simple but fun spreadsheet that gives students a chance to explore the definition of an outlier that uses the IQR. Used in the whole class setting, students’ intuitions about what is likely to be an outlier can be offered up through a range of different problems.

• This allows students to set each other questions where coding is a great help in finding the answer. Much of the important detail can be hidden at the start, and then revealed later. All the awkward calculations are done by the spreadsheet.

MSV 21: Spot the Errors

• 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.

MSV 9: Do we divide by n or n-1?

• The definition of ‘variance’ is always a hard thing to tackle. There is going to be a certain amount of messiness in any explanation, especially when books and calculators never seem to agree. This spreadsheet and accompanying notes hope to make this topic as clear as possible whilst remaining at the right level for AS students.

MSV 12: The Barchart

• Here is a chance to cut up bars in your head and reorganise them in various ways. The mean, median and mode and the various ways in which they might be ordered are all part of it.

MSV 24: Quartiles for a Small Data Set

• Tackling this topic is often a rather unsatisfactory affair. There are different rules for doing this according to which text you read. The rules used here are those suggested by MEI, which seem most sensible to me. By the end of this exercise, students will hopefully have the idea that quartiles and small data sets don’t really mix!

MSV 28: The Five Dice

• This activity invites students to play with the definition of mean, median and mode in the context of a small data set. It could be argued that this is more number theory than statistics; the ‘puzzle’ element is strong here.

MSV 29: Measures of Location

• I confess there is nothing terrificly imaginative here; but in case you find it useful, this is a worksheet that covers all the different situations in which calculating measures of location might be required, including ‘age’, ‘to the nearest’, and ‘up to and including.’

• A discussion document, with a range of possible ways to measure spread. I am not going to patronise you with the answers here!

#### 3. Probability

MSV 27: The Independent Events

• Proving or disproving that two events are independent is always a tricky corner. Venn diagrams are often the best way to approach this, as here. The result contained in this activity is surprising for a moment or two, before the logic sinks in.

MSV 32: Biassed Independence

• A simple problem about independence with an ordinary dice becomes more interesting if we allow the dice to be biassed…

#### 4. Discrete Random Variables

MSV 5: DRVs from a Bag

• I enjoy taking a bag of numbers and looking at the possible ways to fit them into some setting or other. Here I wonder how a bag of numbers might fit into a probability distribution table.

• A simple idea; how does rolling a dice and doubling differ from rolling two dice and adding? Excel comes to the rescue here, and no real dice have to be found.

MSV 23: The Two DRVs

• Another task or ‘puzzle’ that looks at a statistical idea in a pure mathematics kind of way. Quite hard work for all except the most able.

MSV 26: The Three Dice

• Let Excel take the strain while you explore the mean and variance for these dice. Sooner or later you are going to want to try out a little theory, in which case Sheet 3 of the spreadsheet could be a help.

MSV 31: Tetra-dice

• I’ve explored this kind of problem already, but maybe there is a simplicity about the task here that is an improvement. Can a four-sided dice with positive integer faces including odd numbers ever have expectation and variance the same?

#### 5. Binomial Distribution

MSV 3: Most Likely Value

• This activity offers a slightly different slant on the standard question, “What is the most likely value for a Binomial Distribution to give?” Some of the nuances here are quite tricky, and might be appreciated more by the top end of your group.

MSV 11: Binomial Reverse

• Sometimes a problem becomes a lot more interesting when turned around the other way. Here is a standard (and maybe a little dull?) Binomial question that livens up when reversed.