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 [email protected] 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.

3 Comments on "Average not normal"

  1. Ronald Sharrad Jones | November 24, 2021 at 2:43 pm | Reply

    Johnny would need to ride faster than the speed of light, but anything short of an instantaneous return will not suffice.

  2. Nathaniel Jewell | November 25, 2021 at 6:11 pm | Reply

    Infinite. Poor Johnny can’t pull it off.
    I know this all too well because, 30-odd years ago, an equivalent question provided my comeuppance as a maths-loving Middle School student:
    Challenge question: A car drives up a 1km hill at 50 km/h. What speed must it average over the 1km downhill section in order to average 100 km/h for the combined trip?
    150 km/h, I replied confidently.
    Oops.

    And that reminds me … Once, back in 2003 (coinciding with my move to Mt Barker from Strathalbyn), you idly raised a nautical conundrum:
    Suppose you buy a boat and replace every one of its components. By the end, is it the same boat?
    To my shame, I never got around to responding. So here goes, a mere 18 years late:
    Your thought experiment has actually been performed – by legendary 20th century yachtsman Sir Francis Chichester when he decided to ‘settle down’. Sir Francis’s insurer was, of course, Lloyd’s of London. And Lloyd’s insisted it was the same old boat in new clothes.
    So there’s your answer: Yes – and that’s official.

  3. You have posed a trick question about Little Johnny.
    Since his average speed getting to school was 15km/h, it took him 4 minutes to travel the 1km distance.
    To average 30km/h for the whole trip, he would need to cover the 2km distance in 4 minutes, but since he took 4 minutes to get to school, there is no time left for the trip home! So the answer to the question of how fast does he need to go to average 30kph for the trip is: it can’t be done!

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