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What is estimation?
We sometimes think of an estimate as just a guess. In mathematics, it means something a bit more useful - an educated guess. Even though the answer isn't exactly known, with estimation, you can not only give a good approximation, but also, you can give an idea of how close your estimate is to the 'true' answer.
For example, suppose you want to buy some music CDs for a gift. You have $50 to spend and you know CDs range in price from about 8 to 12 dollars. What's a good estimate for how many you can get? Well, if you get them all at $8, you can get 6.
On the other hand, if you just buy the more expensive CDs, you could only buy 4. In this example, your estimate would be, "I can buy at least 4, but no more than 6."
You don't have an exact answer, but you have a realistic range - an educated guess.
How is estimation used in the real world?
Estimation is used anytime we deal with quantities that aren't exact or when we want to make a prediction about an uncertain future. When businesses bid on contracts, they guess at their costs for materials and labor and create a bid based on this estimate. Prices for supplies might change, the job might be more difficult or easier than they expect... estimation is the only tool available.
Another common use is when talking about a measurement that is uncertain. When you see a poll on the news, they will give an error estimate, usually as: plus or minus X percent. This means they are not claiming their poll numbers are exact, rather, they are claiming the actual answer to the poll question lies between a certain number above (plus) and below (minus) the number given. What the poll-taker is telling you is how good he thinks his estimate is.
A basic problem in estimation.
One problem that arises is how to combine two or more estimates. Suppose you have a flock of sheep that are "about a hundred". (You don't know exactly, some sheep might have been eaten by wolves and some lambs might have been born.) Your best estimate is 100 +/- 10. The symbol +/- is read, "plus or minus".
Let's say you buy your neighbor's flock that has 100 +/- 5 sheep (he has a better estimate than you). The question is how to add these two estimates together to get an estimate of the combined flock of sheep?
Since you could have as many as 110 sheep and he could have as many as 105 sheep, the total could be as high as 215. On the other hand, he could have as few as 95 sheep and you could have as few as 90 which would total 185 sheep when put together.
The way to express this is to add the estimates and add the errors, so that your new estimate will be 200 +/- 15. Errors in estimates are always added this way. They never decrease when you combine estimates.
Who invented estimation?
You might think that guessing is as old as mankind. This is surely so. But mathematicians are still working today to discover new methods. So, while no one gets credit for inventing estimation, ways to get information about uncertain quantities are still being invented today.
An interesting fact about estimation:
One of the most famous estimates is an attempt to guess at the number of alien civilizations around that we might be able to communicate with. Yes. Aliens, ETs´, spacemen.
Called the Drake Equation, the estimate was formulated by Dr. Frank Drake, an astrophysicist. The formula has seven different estimates built into it that all combine to form the final 'answer'.
Drake´s original estimate, in 1961, was 10. A more recent estimate gives 2 as the best answer.
His formula has received a great deal of criticism, because each of the seven estimates in the formula (that have to be combined together to get a final answer) are disputed and even the amount of error in most of them cannot be known accurately. But it is still a wonderful example of how an educated guess, or estimate, is constructed.