🌱 A garden where numbers grow
The Average Machine
Everyone knows the ritual. Almost nobody knows what the number means.
Everyone knows the ritual.
Add them up, divide, write it down.
Almost nobody asks what the number means.
The set-up
Five friends, one pile of sweets
Here’s what that ritual number is: the mean is what everyone would have if you shared the whole pile out evenly. That’s the entire idea. Once you can see it, you can also see when an average is lying.
Five friends brought sweets to the cinema: 2, 3, 5, 6 and 9. The dashed line is where they’d all land if you dealt the pile out equally.
Your turn. Drag a tower up or down (or use the buttons), then hit share, and watch where everything settles.
The dashed line is the fair share: the level everything lands at if you deal the pile out equally. Change any tower and it moves instantly. That line is the mean.
The mean isn’t a rule you memorise.
It’s the level a pile settles at when you share it out evenly.
The trap
Does anyone have to be average?
Those five towers average 5. Quick question, and answer before you peek: if five numbers average 5, does at least one of them have to be 5?
One number can bend the whole thing.
Send it far enough out…
…and the average chases it, alone.
The wrecker
One kid can drag the whole average
Five kids get pocket money. Four of them get €5. The fifth is Jo. Before you touch anything: if Jo’s money climbs to €100, where does the mean end up? Pick a number, then drag Jo’s bar and watch.
Strip it right back. You’ve got €5. Your mate has…
The machine is only two moves.
Pile up. Deal out. That’s all of it.
Doing the sums
The machine: pile up, deal out
The whole machine is two moves. Pile up: add every number into one total. Deal out: share the total between however many numbers there are. Edit the values and watch the working, including the tempting wrong move, crossed out where it belongs.
Smallest possible machine. Two numbers: 4 and 10. Pile up: 4 + 10 = 14. Deal out between 2: 14 ÷ 2 = 7. Picture it as towers: slide 3 blocks off the 10 onto the 4 and they level at 7 each. That levelling is the divide. The machine never does anything cleverer than that.
The machine runs in reverse: mean × how many = total. So 6 × 4 = 24. You can’t know which four numbers (could be 6, 6, 6, 6 or 1, 2, 9, 12), but the total has to be 24. Anyone who tells you their four test scores “average 6 out of 10” has told you their total whether they meant to or not.
Every average is the same machine.
A pile, shared out evenly…
…whether or not any real day, game or person matches it. Goals per game, screen time, rainfall for July: once you can see the share-out, you can see when it’s quietly lying.
One more thing
Next time someone quotes you “the average family has 2.4 children”, don’t smirk. Explain it. Total children, shared between total families; nobody has 0.4 of a sibling and nobody needs to. And when an average sounds surprising, you’ve now got the first question to ask: what’s the biggest thing hiding in that pile? Explain to someone why a made-up number can still be dead useful, and you own this one for good.