I have used this activity several times now throughout my career and I must say I always enjoy using this.
Be prepared for a few lessons where things may feel somewhat chaotic but the truth is there is so much value in this activity.
When I stop and think about how statistics is generally taught, I realised that I don’t really introduce the idea of larger data sets until A-Level. Our students are used to us presenting data in perhaps already grouped forms or with raw data that is actually quite simple i.e. a row of numbers that need averages finding. We don’t really give them data to analyse that could resemble something closer to real life; enter lives of presidents.
To see what I mean, go now to: https://nrich.maths.org/11007
The students are simply presented with facts about the presidents of the united states (see below)
The students are asked to create their own research question and then set about answering their question. What a brilliant task for them to do! This is where you need to be prepared for the little bit of ‘chaos’. Now you may be thinking that this is a process that our students should be used to from science, and I would agree, but I also know that some students find it hard to make that link. So straight away this process allows for a link to be made between similar processes in science: make a hypothesis, go about testing it, make a conclusion.
What is interesting is that some students find it difficult to create a question. Nrich have themselves suggested lines of inquiry and so I always put these on the board as a possible option.
Some of my students choose one of these questions to research where as others create their own lines of inquiry.
I then set about visiting the pairs of students asking what it is they are researching and asking how they are going to go about this. I am also on hand to answer questions they may have e.g. should I draw a scatter graph for relationship? Can you remind me how to calculate what degrees I need for a pie chart? etc
Apart from that, I allow the students some freedom to go about their research and give them an opportunity to experience what it feels like to be presented with a sea of data and make some sense out of it.
Some great conversations come out of doing this project. One group was looking into the age of deaths of the presidents and decided to group the presidents based on the year of inauguration. Below is their grouped frequency table:
You can see that the average age of death goes down between being inaugurated in 1860 to 1900 and so I asked them why they thought this might be. They told me that 3 of the 4 assassinations had happened to the presidents in this group and so this was clearly affecting their data. We then discussed what skew meant and that data can only highlight that something has happened but you need to look elsewhere to find why (cause and effect). We then also discussed that it could be possible to state that there were anomalies at this time and that they could take these anomalies out and re-evaluate the data to see if there actually is a genuine dip at this point or it these 3 presidents were having a major affect. From there a discussion about which averages are the best to use in different situations is possible. I know this group had used the mean and so I am hoping that next lesson they may re-evaluate this as a whole and take other averages to compare. If not, that is a direction I can suggest to them.
This activity is certainly adaptable to all year groups based on what knowledge of data handling they have. I have done this activitiy with years 8 to year 10s and just encouraged them to use different representations of data e.g. with year 10 they drew box plots and cumulative frequency diagrams with my current year 8s they are producing pie charts, scatter graphs and frequency polygons. There is so much that can be done with this data and the fact that the task self differentiates is brilliant. I highly recommend using this next time you are doing a statistics topic and allowing the students to get a sense (all be it a small one) of what it is to be presented with larger data and research a question.
Examples of my year 8s work is below: