How to solve Intervals questions
Estimate a number with a lower and an upper bound. You score lower divided by upper if the true value is inside, and 0 if it is outside. You can type 340m, 1.5b or 3e8.
How to solve them
- Score: lower / upper if the true value is inside your range, otherwise 0. A lower bound of 0 always scores 0.
- Width rule: if you can compute it (seconds in a day), use almost no width. If you know the order of magnitude but not the digits, aim for upper/lower of about 1.3 to 1.6. If you are guessing, go 2 to 3 times wide.
- Method: anchor on a fact you know, then adjust. US population 340 million, Earth circumference 40,000 km, Earth to Moon 384,000 km, light speed 300,000 km/s.
- Check: would you bet that the truth is inside? Aim for roughly 80 to 90 percent of your intervals to contain it. The overview tracks this for you.
Worked examples
Estimate the population of Los Angeles (city). Give a lower and an upper bound.
Answer: 3,800,000 people
- True value: 3,800,000 people.
- About 4 million.
Estimate the circumference of the Earth at the equator. Give a lower and an upper bound.
Answer: 40,075 km
- True value: 40,075 km.
- The metre was once defined so this is about 40,000 km.
Estimate the mass of the Moon. Give a lower and an upper bound.
Answer: 7.35e+22 kg
- True value: 7.35e+22 kg.
- About 1/81 of the Earth.