# What interesting data manipulations can be done over 70x5 data points in a school context?

TL;DR: I am looking for ideas for a school assignment in basic statistics.

Context: My son (14 years old, French class 3ème, equivalent to 9th grade) got a group assignment in Mathematics.

They have biometric data (the heart and breath rate 3 minutes after having ran for a given time, and the distance - as well as the sex), collected for 70 children. They have some latitude to use this data to make a point.

They decided to look at the differences between sexes for the various categories of data. Since they did not have any real statistics yet, they want to "take the average in each category, and draw conclusions on the differences between sexes" (more or less quoting them). This would correspond to what they learned at school so far (averages and medians).

This would probably be enough for their assignment (it matches their expected level) but I would like to push them a bit more. They are a bright bunch of kids and I would like to use the opportunity to open they eyes a bit more on what can be done with such data.

My question: what other interesting analysis can be done with this data? (I am ready to teach them a bit so that they understand, I have a rudimentary understanding of statistics thanks to my PhD in Physics, but it was long ago).

• to have them draw the distributions (3 categories x 2 sexes) and discuss them: is there a shape that fits, and if it looks like a Gauss distribution - why could it be so (something I am not really sure yet myself but I will dig into that). Also - what kind of experiment could lead to another shape.
• let them discover that by merely comparing the averages, one cannot draw a fool-proof conclusion. I will need to dig into how to calculate the uncertainty but this is rather for me than for them (I would just tell them that there is an uncertainly and find some reasonable analogies)
• I would ask questions about the overlaps of the distributions and what this can mean (this is linked to the uncertainty point above)

I would appreciate any other idea (which can be less mathematically oriented - I was thing about some data mining but the sample is way too small). Please keep in mind that they are 14 years old (but very interested and bright).

As an afterthought, I would also use the opportunity to mention how important in science it is to have your statistics right and how this can be used to manipulate results (The Bell Curve could be one example, I would find more)

• Start with something basic. How does the heart rate and breath relates to the distance covered or the speed of the runner. Then go on towards more complex things like making inference of which people are more prone to cardiac problems by analyzing the variations in heart rates. – show_stopper Mar 19 at 20:02

• This is an excellent idea - I do not know R but I code in Python and they have some basis (my son at least). A Jupyter notebook coupled with numpy should be an interesting ride. – WoJ Mar 19 at 20:20