Scatter Graphs

This weblog is becoming a fleck statistics-heavy, which is ironic given that I don’t specially similar pedagogy statistics at Key Stage iii as well as 4.  I much prefer pedagogy algebra. I’m also quite peachy on surds as well as indices. And I similar trigonometry. In fact, apart from the strange annoying-to-teach topic similar loci as well as constructions, I’d seat most information treatment topics correct at the bottom of my ‘things I relish teaching’ list. It never fails to amaze me how long roughly teenagers receive got to plot a graph. What a faff.

Anyway, this postal service is all most ideas for pedagogy scatter graphs. And I retrieve to follow it upwards alongside a postal service looking at applications of box as well as whisker plots exterior the maths classroom.  But as well as thus I’ll halt alongside all the statistics.

Practical activities

Unusually for a maths lesson, there's opportunities for roughly practical activities when nosotros innovate scatter graphs. The obvious sentiment is to receive got students plot meridian or manus bridge against shoe size. If you lot desire to acquire fifty-fifty to a greater extent than practical, attempt a human scatter graph inward the classroom or inward the playground (using chalk axes).

Outliers 

I similar to purpose the ii scatter graphs shown below (stolen from a Ten Ticks worksheet) inward a shape give-and-take most outliers.  Ask your shape what could receive got caused these extreme values as well as you'll in all likelihood acquire roughly actually creative suggestions!

Line of Best Fit

I instruct my students to depict a trouble of best stand upwards for yesteryear trying to minimise the distances betwixt all the points as well as the line. That’s what a to the lowest degree squares regression does. Contrary to pop belief, at that spot doesn't receive got to live the same release of points to a higher house as well as below the line. Nor does the trouble receive got to become through whatsoever of the points. And the trouble sure enough doesn't receive got to become through the origin. Beware of dodgy methods taught inward other subjects. This misconceptions activity yesteryear frickard on TES is helpful - I've used this inward a 'hands on caput if you lot retrieve it's true, hands on hips if you lot retrieve it's false' activity.

Impossible Predictions

'Extrapolation' from regression lines is something that comes upwards at Influenza A virus subtype H5N1 level, only the sentiment tin terminate brand for interesting discussions at Key Stage iii or GCSE. The telephone substitution signal is that fifty-fifty if nosotros detect a linear human relationship inward the information we're examining, nosotros can't assume that human relationship extends beyond the make of the data. Here's a dainty instance for shape discussion:

The graph below shows a negative correlation betwixt twelvemonth as well as fourth dimension taken yesteryear athletes to run 100m. It suggests that the speed of 100m runners has increased over time. Influenza A virus subtype H5N1 trouble of best stand upwards for has been drawn. Why produce you lot retrieve 100m runners are getting faster? Do you lot retrieve this tendency volition continue?

Possible reasons for the increment inward speed include: advances inward technology (ie to a greater extent than lightweight or streamlined clothe as well as trainers), inquiry into optimal diets as well as grooming plans, sponsorship important athletes receive got to a greater extent than fourth dimension to train, the introduction of starting blocks inward the 1940s as well as an improvement inward the accuracy of timing the race.

If the tendency continues indefinitely (ie if nosotros depict the trouble of best stand upwards for into the future) as well as thus at roughly signal people would live able to run 100m inward null seconds, which is impossible. There must live a signal at which the fourth dimension volition plateau, due to limits inward humans' physical capabilities. Although at that spot is a linear correlation, nosotros must live careful non to brand predictions inward the yesteryear or futurity because the linear human relationship is over a express fourth dimension period.

The graph comes from this Minitab Blog post as well as the sentiment was seat into my caput yesteryear Kings College London PGCE tutor Chris Olley. 

"Wind is caused yesteryear the rotation of windmills"

I love the causation vs correlation discussion.  It's a real of import learning signal for students who volition come upwards across all sorts of dodgy statistics inward everyday life.

doubt.it

Influenza A virus subtype H5N1 typical instance is shoe size as well as reading age. The ii variables are positively correlated, only apparently the size of someone's feet has no demeanor on on their reading ability. For to a greater extent than ideas banking concern check out this spurious correlations website.

If you're planning a shape give-and-take on causation as well as thus receive got a quick read of 'Correlation does non imply causation'on Wikipedia (not e'er the best source only gives roughly skillful examples).

Correlation does non imply causation, only it does waggle its eyebrows suggestively as well as gesture furtively spell mouthing "look over there". – xkcd 

Resources

Finally, here's a few resources that you lot could purpose inward your lessons:

• I love this Bee Aware action from Don Steward. It could easily live made into a mini-project/display move most the campaign as well as demeanor on of the demise of dear bees.
• The first-class Mathematics Assessment Project gives us ii tasks - Scatter Diagram and Birds' Eggs
• There's no shortage of real-life applications of scatter graphs. This worksheet 'Shake It Up alongside Scatterplots' is 1 of many examples (here's the solutions).
• Nrich gives us this nice David as well as Goliath activity.
• 'Foldables' seem to live a big matter inward U.S.A. math lessons, only I've never seen them inward the UK. I retrieve my students would quite similar them. Here's an sentiment for correlation foldables from the weblog 'Everybody is a Genius'.
• I similar this online tool for checking the accuracy of lines of best stand upwards for from Mark Ritchings
• Here's an interesting group project. I similar the sentiment of giving each pair/group ii options thus they tin terminate select the variables they prefer, as well as that everyone inward the shape is working on something different. Also, the 'assigned tasks' for each grouping fellow member (see in conclusion page) is an sentiment I haven't seen earlier for organising grouping work. These detail tasks may non live suitable for a United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland lesson because nosotros don't hold off students to calculate the equations of lines of best fit, only the sentiment could live adapted.

I promise this postal service has been helpful.  Please comment if you lot receive got whatsoever ideas to share. 

By the way, this cool moving scatter graph is worth a look.

xkcd.com

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