Slashdot Mirror
How Well Do You Estimate?
A random UK blogger has published a quiz asking readers to estimate various numeric values which they may or may not have knowledge of; and has analyzed the resulting answers to determine how well people guess. The first part of the results looks at some specific questions, and the second part takes a look at the quiz overall.
Reminds me of a bit of training from my army days.
If you have difficulty estimating a distance ( range), divide the distance in two, and try estimating that.
This sounds stupid, but actually works. Well, it worked for me. I'll never forget how I laughed in my head at the suggestion, and my astonishment at it actually working.
Mike.
I used to work at a small datamining shop. The people there were very bright, some of them quite famous in the fields of statistics, number theory, etc.. One day, we were sitting in the front room of our offices having lunch, chewing the fat, as it were.
At lunches, we would sometimes try to stump our CTO a grey beard who is famous for work in information theory and general genius. We had never succeeded, even with obscure questions in biology "How do Prions work?", physics "What order are the colors of the rainbow, and why?", "How does the Corriolus effect work?", etc. that none of us had any particular knowledge of, and always had to research afterwards to determine the correctness of his answers.
So, I posed the question to the group "How many leaves are on that tree outside the window?" It was a ~30 foot tall, bushy tree in the height of summer. I hoped he'd take the bait.. I thought this was going to be very hard to "get right", and it would even be difficult come up with a plausible answer.
After a few moments, I set off the responses by saying that I thought it easily had 10k leaves, possibly 20k or more.
Everyone gasped. "Oh no! No way..." and then proceeded to offer lower and lower estimates.
The responses started with me and made their way up in the seniority ranks (I was the most junior) all the way up to the CTO. He said "Oh! those kinds of things are notoriously hard to estimate. We typically overestimate grossly in counting things of plentitude. Oh, I don't know. 200?".
Finally we had him. There was no way there were 200 leaves on that tree.
Later, in discussion, a trend became clear. The more senior the person, the more conservative was their response, even to the ridiculous level of our CTO saying a tree in full flush, that he could see right outside of the window, had 200 leaves, when it most plainly had many, many more.
Anyone want to hazard a guess? How many leaves on say, an adult Sycamore (or Maple, Oak, etc.)?
Substitute +2 and 0 for low karma posters, obviously...
Looking back on my posts, I have shedloads of +5s and occasional -1s in a long list of +2s... but very few +3s. Moderation is a runaway process, in which the difference between +5 and -1 is a single modpoint.
Real Daleks don't climb stairs - they level the building.
As almost every single comment up until now talks about personal experiences or makes stupid jokes, I'm going to critique the method he uses to score an answer. From the second link (find a google cache of it to read it) you can see that he treats each answer and estimate of the accuracy of the answer as a single question - you get a single score from both. I think this approach is fundamentally flawed. Why not instead score the guess (with some sort of algorithm like the one he uses) and then score the guess of accuracy by the same method. Then if you want a single number, add the two together. Right now if you guess well and guess your accuracy perfectly, you get zero points. That is completely out of whack. Instead, using my way you score the best possible score when you guess perfectly and perfectly guess your accuracy, and the worst possible score when you guess horribly and horribly guess your accuracy. The scores move between those two extremes rationally too. As he wanted people who guessed zero error (thought their guess was a perfect guess) to get no points, he obviously had an agenda - that people should be penalized for thinking they are perfectly right. In no way is this an unbiased or useful test.
I submitted this story last night, and it didn't get posted.
They spend a lot of time on grouping. For example What is 97 + 198? I was taught to add 8 and 7, carry the one etc...
They are taught to group the numbers, the instantly recognize that the answer is close to 300, then see how it differs from the 100s. 97 is 3 less, 198 is 2 less. Now add the 3 and 2, getting 5.
The answer is of course 300 - 5, or 295.
I find this method very intuitive.
I estimate that I would end up somewhere in the middle.
:)
You must not be an American then
Take for example graduating from college. Did you know that there are no "below average" college graduates? Proof: In order to graduate from college you must have a GPA equating to a C or better. A C is average, therefore there are no below average college graduates.
Other estimates that I ask people from time to time. What percentage of the US population is African American (black)? What percentage of the US population has a college degree?
Although the African American question is a little skewed because of the area I live in does in fact have about 30-40% of the population as being black, the national average in 2002 is 13%. I typically get answers that the national average is 30-40%.
The college degree question is also very off. I typically get answers around 50% or higher, where its 27% as of 2003. Its some kind of myth here in the US that everyone has to go to college so they can do unskilled labor the rest of their lives. In fact, my aunt was lecturing her (adult) son that got his girlfriend pregnant with the "How are you going to pay for the kid to go to college?" routine. When neither of her parents went to college, neither her nor her husband went to college, and none of her 2 children went to college.
Ask an American and a Japanese if they are "good in math". The Japanese will typically say "no", the American will say "yes". Ask the same 2 kids to take a standardized math test, the Japanese will score better than the American.
However, although its important to feel good, its more important to look good!
On a side note, there are many errors made when newspapers, magazines, etc. estimate numbers. Sometimes they will round values before presenting the final number, causing a huge difference. Or they will give some value like $6,021.50 when some of the values have only two or three significant digits. Or they'll make some hideous stats error such as adding two means together and not weighting the scores appropriately. An excellent book that discusses this is John Allen Paulos' "A Mathematician Reads the Newspaper."