What is estimation?

0:47 Welcome to Maths Is Not Boring by Kidopoly.com. I'm Mira! And I'm Finn. If you haven't already, tap follow wherever you're listening so you never miss an episode. Okay, Mira, what are we looking at today? Imagine a giant glass jar stuffed to the very top with sweets. You have to guess exactly how many are inside to win a prize.

1:11unknown Ha!

1:12 I always try that, and I'm always completely wrong. I either guess way too few, like 50, or a million.

1:20 Most people are. If you just ask one person, their guess is usually way off. It's just too hard for one set of eyes to perfectly count hundreds of things stuffed in a jar. But if you ask hundreds of people and put all their wrong guesses together, something impossible happens.

1:42 Impossible how? Like they magically form the right number.

1:46 Exactly that! The crowd somehow knows the right answer, even though almost nobody in it does. Today we're talking about a famous moment when a crowd of regular people guessed the weight of a giant ox, and how their wrong guesses added up to an unbelievable truth. We are talking about estimation. An estimate isn't a wild random guess, like just saying the first number that pops into your head.

2:15 It's a sensible guess based on what you can see and what you already know.

2:20 Like looking at a stack of books and estimating it's about as tall as my dog. I know how big my dog is, so I can make a good guess.

2:29 Exactly! You are using a clue to get close. But this story takes estimation and turns it into magic. It takes place a long time ago, in the year 1906.

2:42 Whoa, over a hundred years ago! People were riding in horse-drawn carriages and wearing top hats.

2:49 In a seaside city in England called Plymouth, there was a huge bustling country fair going on called the West of England Fat Stock and Poultry Exhibition.

2:59 That is a very long name for a farm show. Did they just show off big chickens and cows?

3:05 Pretty much. It was full of noisy animals, farmers, butchers, and lots of regular people just enjoying a day out. It was a really exciting, crowded place. And what were they looking at? Right in the middle of the fair was a massive, heavy ox. People were crowding around it, paying a tiny coin called a sixpence for a little ticket.

3:28 A ticket to do what? Pet it? Ride it around the fairground?

3:33 No, to guess its weight. Specifically, what it would weigh after it was butchered and dressed for the market. Whoever gassed closest would win a prize.

3:43 That sounds really hard. Did they have scales to check? No scales, just their eyes, their brains, and a little piece of cardboard to write their guess on. So who was the person paying attention to all this? Was he guessing too?

3:58 A scientist named Francis Galton was visiting the fair. He was very curious about how ordinary people think, and he decided to collect all those little ticket cards after the contest was over to see what he could learn.

4:12 Wait, why would he want hundreds of pieces of cardboard with wrong guesses on them? Didn't he want to find the smartest person?

4:20 Because he wanted to see just how wrong a crowd of regular people would be. There were expert farmers and butchers there, but also clerks, shopkeepers, and people who knew absolutely nothing about farm animals.

4:32 Haha, that would be me. I would just write down a million pounds.

4:37 Some people probably guessed way too high, and some guessed way too low. In total, after throwing away a few cards that were too messy to read, Goulton had 787 readable guess cards.

4:51 787? That's a huge stack of tickets to carry home.

4:57 He took all 787 cards and did something very simple but very special. He didn't just look at the winner, he laid them all out and put them in order, from the very smallest guess all the way up to the very biggest guess.

5:13 Okay, so I'm picturing a huge line of cards stretching across a room. The tiny guess at one end, the giant getters at the other end. Exactly.

5:22 And then he walked right down that long line of cards to find the one sitting in the exact middle. The card with an equal number of guesses below it and above it.

5:33 Why the middle one? Why not the highest or the lowest?

5:37 In maths, that middle number is called the median. Goulton thought that middle guess would represent the whole crowd perfectly, without being ruined by one or two completely wild guesses. He even called it the voice of the people.

5:52 Okay, the suspense is killing me. I have to know. What was the middle guess and what was the real weight of that giant ox?

6:01 The true weight of that ox, when it was finally put on the scales and measured properly, was 1,198 pounds.

6:12 That is so heavy! Almost 1,200 pounds! I can't even imagine lifting something that big.

6:18 Yes! Now, remember, there were 787 people guessing, and almost nobody got it exactly right. But Galton looked at that middle card, the median of all those guesses.

6:33 And? What was written on it?

6:35 The middle guess was £1,207.

6:41 Wait, hold on. The real weight was £1,198, and the middle guess was £1,207? That is incredibly close.

6:53 Yes! Out of an animal that heavy, the crowd's middle guess missed by only nine pounds. That is less than a 1% difference.

7:03 But that can't be right. How can hundreds of people who don't know the answer suddenly know the answer when you line up their cards? That sounds like a magic trick.

7:13 That is the beautiful thing about it. It's not magic. It's just how numbers work when you gather enough of them. The people who guessed way too high perfectly balanced out the people who guessed way too low. All those wrong guesses cancelled each other out, leaving only the truth in the middle.

7:32 That is wild. It's like the crowd itself is a giant brain, and all the little mistakes just wash away.

7:39 It really is. And here is something even cooler. Later on, other people did some more maths on Galton's numbers. They worked out the mean, which is a different way of looking at a group of numbers, and it came out to £1,197. Even closer! But Galton stuck to his middle card, the median.

8:03 I am definitely trying this the next time I see a jar of sweets at a school fair. I'll just ask 50 people for their guess, line them up, and find the middle one. I'll win every time.

8:14 You absolutely should try it. Galton was so amazed by what he found that he couldn't keep it to himself. He wrote a whole report about it in the year 1907. What did he call the report? He published it in a famous science magazine called Nature, and he titled it Vox Populi. That's a Latin phrase that means the voice of the people.

8:40 It really changes how you see things, doesn't it? Like, a crowd of people might look loud and confused, but underneath it all, if you just listen to the whole group, they might know exactly what's going on.

8:52 Yes, that's why sharing many guesses is so powerful. It's how a lot of things work today. Modern weather forecasts use this exact idea. Computers make lots of different sensible guesses about the weather, and scientists put them all together to get closer to the truth.

9:12 Ooh, or like a quiz team. One person might not know the answer to a tricky question, but if everyone talks it out and shares what they think, the team suddenly figures it out.

9:22 Exactly! Every single one of us has a little piece of the puzzle. When we bring our estimates together, we become incredibly wise. Alright Finn, quiz time! Let's see what you remember about the wisdom of the crowd.

9:37 Okay, I'm ready. I've got my estimating brain switched on.

9:41 First question, what year did this famous fair take place? Next one, in what English city was the country fair held? Question three. How many readable guess cards did Galton put in order? Here's number four. What was the middle guess or the median in pounds? Last question. What Latin phrase did Galton use for the title of his 1907 report, meaning the voice of the people?

10:27 Great job! Let's see how you did. The first answer is the fair took place in the year 1906. For question two, the fair was held in the city of Plymouth. Number three, Goulton lined up 787 readable guess cards. For question four, the middle guess, the median, was £1,207. And the final answer is he titled his report Vox Populi.

10:59 I am still just thinking about all those little cards laid out on a table, pointing straight at the real weight of that ox. It feels like magic.

11:09 I know. It makes you look at a crowd of people totally differently, doesn't it? The truth is hiding right there in the middle of all of us.

11:19 Hey, if you enjoyed guessing the weight of an ox with us today, could you do us a huge favour? Leave us a five-star review.

11:27 Yes, it really helps the show. Just scroll down in your app and tap the five stars. It's much easier than estimating an ox's weight.

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11:57 See you next time on Maths Is Not Boring.