Scatter Graphs

This weblog is becoming a fleck statistics-heavy, which is ironic given that I don’t peculiarly similar instruction statistics at Key Stage three in addition to 4.  I much prefer instruction algebra. I’m also quite dandy on surds in addition to indices. And I similar trigonometry. In fact, apart from the strange annoying-to-teach topic similar loci in addition to 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 accept to plot a graph. What a faff.

Anyway, this ship service is all nigh ideas for instruction scatter graphs. And I intend to follow it upward amongst a ship service looking at applications of box in addition to whisker plots exterior the maths classroom.  But in addition to hence I’ll halt amongst all the statistics.

Practical activities

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

Outliers 

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

Line of Best Fit

I learn my students to depict a employment of best check past times trying to minimise the distances betwixt all the points in addition to the line. That’s what a to the lowest degree squares regression does. Contrary to pop belief, in that place doesn't receive got to live the same seat out of points to a higher house in addition to below the line. Nor does the employment receive got to become through whatsoever of the points. And the employment for certain doesn't receive got to become through the origin. Beware of dodgy methods taught inwards other subjects. This misconceptions activity past times frickard on TES is helpful - I've used this inwards 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 upward at Influenza A virus subtype H5N1 level, simply the watch tin brand for interesting discussions at Key Stage three or GCSE. The cardinal shout out for is that fifty-fifty if nosotros bring out a linear human relationship inwards the information we're examining, nosotros can't assume that human relationship extends beyond the attain of the data. Here's a prissy instance for class discussion:

The graph below shows a negative correlation betwixt yr in addition to fourth dimension taken past times athletes to run 100m. It suggests that the speed of 100m runners has increased over time. Influenza A virus subtype H5N1 employment of best check 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 inwards speed include: advances inwards technology (ie to a greater extent than lightweight or streamlined wearing clothing in addition to trainers), query into optimal diets in addition to grooming plans, sponsorship important athletes receive got to a greater extent than fourth dimension to train, the introduction of starting blocks inwards the 1940s in addition to an improvement inwards the accuracy of timing the race.

If the tendency continues indefinitely (ie if nosotros depict the employment of best check into the future) in addition to hence at roughly shout out for people would live able to run 100m inwards null seconds, which is impossible. There must live a shout out for at which the fourth dimension volition plateau, due to limits inwards humans' physical capabilities. Although in that place is a linear correlation, nosotros must live careful non to brand predictions inwards the past times or time to come because the linear human relationship is over a express fourth dimension period.

The graph comes from this Minitab Blog post in addition to the watch was seat into my caput past times Kings College London PGCE tutor Chris Olley. 

"Wind is caused past times the rotation of windmills"

I love the causation vs correlation discussion.  It's a really of import learning shout out for for students who volition come upward across all sorts of dodgy statistics inwards everyday life.

doubt.it

Influenza A virus subtype H5N1 typical instance is shoe size in addition to reading age. The ii variables are positively correlated, simply apparently the size of someone's feet has no comport upon on their reading ability. For to a greater extent than ideas depository fiscal establishment check out this spurious correlations website.

If you're planning a class give-and-take on causation in addition to hence receive got a quick read of 'Correlation does non imply causation'on Wikipedia (not e'er the best source simply gives roughly skillful examples).

Correlation does non imply causation, simply it does waggle its eyebrows suggestively in addition to gesture furtively land mouthing "look over there". – xkcd 

Resources

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

• I love this Bee Aware action from Don Steward. It could easily live made into a mini-project/display move nigh the drive in addition to comport upon of the demise of dearest bees.
• The fantabulous 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 amongst Scatterplots' is i of many examples (here's the solutions).
• Nrich gives us this nice David in addition to Goliath activity.
• 'Foldables' seem to live a big affair inwards the US math lessons, simply I've never seen them inwards the UK. I retrieve my students would quite similar them. Here's an watch for correlation foldables from the weblog 'Everybody is a Genius'.
• I similar this online tool for checking the accuracy of lines of best check from Mark Ritchings
• Here's an interesting group project. I similar the watch of giving each pair/group ii options hence they tin pick out the variables they prefer, in addition to that everyone inwards the class is working on something different. Also, the 'assigned tasks' for each grouping fellow member (see lastly page) is an watch I haven't seen earlier for organising grouping work. These item tasks may non live suitable for a U.K. lesson because nosotros don't await students to calculate the equations of lines of best fit, simply the watch could live adapted.

I promise this ship 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