# Statistics

Following last week’s post on Probability, time to check the Statistics content for the new GCSE specification. To start at the beginning again we can look at the Mathematics GCSE subject content and assessment objectives for Statistics; we should also check the Key Stage 3 content to see what we should have done already!

KS3 Statistics Content

KS4 Statistics Content

Note that at GCSE, all students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content. Only the more highly attaining students will be assessed on the content identified by bold type.

Each examination board has clear GCSE specifications, all included in the Further resources section of the GCSE New Content – Resources page. Specimen and Practice Papers provide us with important clues as to how content will be assessed and thanks to the wonderful Mel Muldowney of Just Maths we can see examination questions by topic, which of course includes Statistics. These questions have been collated by Mel as the basis for a GCSE working party set up by the GLOW maths hub. (You can see more on the work of the Maths Hubs here). Whatever we are teaching, referencing the specification, any exemplification documents and also examination questions is essential in understanding how students will be assessed.

There are some changes in content for Statistics if you have been teaching the old specifications; note we have lost specific reference to the Data Handling Cycle as well as Stem and Leaf diagrams. Also missing, I see no reference to stratified sampling for example. We have gained tables and line graphs for Time Series data.

The DfE Key Changes to GCSE Maths document explains ‘No mention of statistical problem solving / data handling cycle’ by saying that it is ’embedded into other subjects such as science and geography where it is explored experimentally’. (I find the phrase no mention of statistical problem solving puzzling).

Looking for further clues on Time Series data, AQA’s Teaching Guidance states that students should be able to:

• understand that a time series is a series of data points typically spaced over uniform time
intervals
• plot and interpret time-series graphs
• use a time-series graph to predict a subsequent value

The sample available (the full document is available to registered members of All About Maths) of AQA’s excellent Teaching Guidance document is in fact the section on Statistics.

We can also see some questions from Edexcel via Just Maths.

From OCR, the very useful series of Check in tests (select link and scroll down the page) includes Interpreting and Representing Data and Analysing Data. OCR’s collection of GCSE Teaching and Learning resources also includes a (provisional) Delivery Guide for Statistics which includes suggestions for activities and resources in teaching Statistics.

From Nrich see the short problems on Handling Data which are based on the UKMT Junior and Intermediate Maths Challenges; problems are available on Processing and Representing Data and there a small number of short problems on Interpreting Data. Longer problems are available in both categories, see Processing and Representing Data and Interpreting Data. As always from Nrich these are excellent resources to get your students thinking, see M, M & M for example, accessible to all and a great example for demonstrating the need for being systematic. Note the follow on problem, Unequal Averages to extend thinking on averages.

The outstanding Standards Unit resources which really help understanding includes some excellent Statistics activities, see S4, S5 and S6. I have often used S4 on Understanding Mean, Media, Mode and Range.

Note the above link includes a PowerPoint to introduce the activity and also gives the solutions. I used the associated software to generate the images for the solutions.

There are numerous examples of Statistics resources in various posts and pages on this blog. David Millward’s PowerPoint collection includes presentations on Statistics.

Guess the Correlation – Omar Wagih

….and to finish, some games!

# Desmos dot to dot

Continuing with my Desmos theme (see the excellent Activity Builder from last week), a happy discovery – you can join plotted points on Desmos. This is ideal for creating cumulative frequency graphs for example – see the example in the following slides.

For completeness, so all the information and examples on Desmos are in one place, I have added pages to the Desmos series.

Note for example a little dancing with Desmos!

# Aural Test – Statistics

My post on using mental tests for revision seems to have interested many readers so I thought I would follow this up. Having looked back in time to GCSE many years ago when an aural test was actually part of the exam (10%) I shall in future refer to these as Aural Tests. It was these tests that started me using the idea of an aural test on anything any time! They can be short and make ideal starters or plenaries or in the case of revision aural tests can last a lesson with lots of associated questions and discussion.

Looking through some old resources I came across a cassette (!) recording of myself reading the questions for a GCSE aural test I recorded for a correspondence college. I intend to transcribe that and will write a post on these old style tests in the near future.

Having successfully given my Year 13 students two aural tests on the Pure Mathematics C3 and C4 modules (after the first they requested the second) my wonderful colleague who teaches the group with me joined in the venture and gave them a third aural test on their  Statistics module. We and our students feel we have done some really useful revision in their last lessons for all three modules on their Advanced Level course.

So this week I have my last lessons with Year 11 (UK age 15-16) who are preparing for their GCSE. I want to look at their Statistics unit with them and have decided that an aural test should work well. Looking at various papers I have extracted some diagrams and asked questions around those. These are topics that I feel my particular class needs; I want to review various statistical diagrams. In case this is of interest I have made all the resources available here. Students need the answer sheet only. The teacher reads the questions and they have to listen very carefully and answer the questions. They will need to write answers in their exercise books or on paper as well as using the answer sheet. With these longer revision aural tests it is sometimes appropriate to give feedback after each question as opposed to waiting till the end to mark all questions. I use both techniques.

Creating the solutions reminded me once again of how useful colour can be to make solutions clear.

I would be interested to hear from teachers who try aural tests with their students; I find them useful for all ages.

# Box Plots with Plotly (& more Statistics Resources)

I have written on Plotly before. I will be revising Statistics with my Year 11 (UK age 15-16) class this week in preparation for their GCSE exam, so the latest Plotly blog post on Three Things That You Can Do To Explain Your Data is very timely.

I plan to use the Nobel Prize Data plots to revise Box Plots and importantly the interpretation of the plots. Whilst outliers are not on the specification for GCSE, they are for the A Level students and I believe that wonderfully clear outlier for for the Noble Peace Prize is worth a mention for all of them!

Note that you can play with the data! If you then choose to Fork and edit, you can save the file so you can modify it for your own use; you will need to create an account (free) or sign in with social media. Choose Traces and you will see several options, you can choose to show points or not for example. Note the Style tab too where you have several options to customise your chart.

Select the link to play with the data

You could use this to create your own charts – simply choose your theme, edit the data and choose your options to create very attractive and clear charts. I like the way the data can be displayed as well and created some simple box plots to demonstrate skew:

For more resources on Statistics see this page, also the worked examples here.

For more resources on Statistics see this page, also the worked examples here.

# World Book Day

Well we may not have World Maths Day this March (it’s in October, and I see from my blog statistics that people are looking for it!) but we do have World Book Day.