Average not normal

I woke up this morning feeling pretty average, once again, and began to wonder if this was “the new normal” I’d heard about?

I mentioned feeling average to a maths geek who said I couldn’t be, since the average man doesn’t exist: I can’t knock on his door and ask questions about his average life. Even if I could, it would be insensitive.

Averages can be misleading because they hide variation. Imagine asking someone who owns an 80kg great Dane and a 5kg dachshund to describe their pets and they tell you that, on average their dogs weigh about 42kg.

I thought this was not a bad analogy until I Googled it and found, with a mix of horror and morbid fascination, that breeding great Danes with dachshunds is a thing that people actually do … I’m guessing for circus side-shows or something like that.

Advertisers know about averages and statistics and they use them in “advertistics” to get their brand into the news. For example a US underwear company did a survey and claimed that, on average, Americans wear their undies for two or more days in a row. But this so-called survey didn’t pass the sniff test because it wasn’t a peer reviewed study. The peers probably refused the gig.

Sometimes you have to dig into a situation to see what is really going on. Consider the following scenario.
Little Johnny lives 1km from school and rides his bike there at an average speed of 15kmh. As he arrives at school a sign says ‘Today is a pupil-free day’. He whoops with joy, turns his bike around, pops a mono, and races back home. The question is: how fast would Johnny need to ride home to average 30kmh over the 2km round trip?

If you have an answer, send it to media@courier.net.au with the Subject: “Average speed”, Tweet @MBCourier #MBCounterpoint or use the comments section below (moderated before comments appear). Three randomly chosen correct respondents will be able to collect a double pass to see Venom: Let there be Carnage at Wallis Cinemas.

– ABK

SOLUTION: Some of our clever readers correctly worked out that Johnny's task was impossible. Read the comments below for explanations as to why that is so. Bruce Camens provides some of the maths behind the solution.