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.

Nrich - 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.