Student generated data

I know many teachers find teaching Statistics at KS3 & 4 a bit dry.  One way to make it a bit more interesting is to make the data somehow relevant to the students.  I’m not talking about football scores or download charts here. I’ve gone to great lengths to source that kind of data and create beautiful resources with it only to find that, while it engages some students, it has the opposite effect on others if it is something they are definitely not into.

So, having given up trying to get down with the kids, here is another approach which involves them generating data so they feel they have some ownership of it.  It’s quick, they can do it in their seats, they get a bit competitive and it’s interesting.

How many dots?

Display this for about 2 seconds.  Tell them what they are going to see and make really clear that they are not to discuss it but write down their estimate.  Then go round the class capturing those estimates on a spreadsheet.  I might use Geogebra for this as it is great a creating box plots, but Excel would be equally good.

You must plead with your students not to cheat and change their estimates from the one they wrote down.  Tell them they will get a second chance.  Do it all again to get a second second set of data.  You now have two sets of randomly generated data that you can use to compare using averages, box plots, standard deviation, etc. It should be a great example of regression to the mean.  Also “The wisdom of the crowd” – always interesting to see how wise your crowd actually is!

Oh, and how many dots? 46. The bare bones of a Powerpoint is here.

The Wisdom of the Crowd

Look, stats isn’t boring! I love doing these Wisdom of the Crowd exercises when teaching averages. Another way of doing it is to display a random scattering of dots on the screen (about 40 or so). Get everyone individually to provide an estimate then calculate the mean.
A really interesting addition to this is to do it once getting everybody to call out their estimate. Then, before calculating the mean, give everyone the chance to change their estimate and record them all a second time.
This can lead to regression to the mean, and standard deviation if you like.
See – stats isn’t boring!

Sir Francis Galton was a statistician in the 19th century. Thanks to him we have concepts such as correlation and standard deviation.  Galton, it would seem, thought through the filter of statistics, a genius who produced hundreds of papers and books on fields as diverse as meteorology, historiometry and psychometrics and who pioneered the use of questionnaires to gather better information for his statistical analyses.

Last week, at my school’s Open Evening, we conducted a mathematical experiment based on one of Galton’s observations.

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Deeper Questions for Mean, Mode, Median

Some quick questions, Powerpoint here.  You could also ask pupils to draw pictures (e.g. scaled bar models) to represent their examples.

And then these to from @. Need a really good explanation!

Other questions:

• What’s the average number of wheels on a vehicle on a motorway?
• What’s the average number of children a woman (in UK, in India, etc.) has in her life?
• What’s the average number of arms a human being has?

Or, if you’re feeling brave: