If you saw the equation 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 and had to come up with a quick estimate of the product of this equation, what would your estimate be? Chances are you’d start with 8 x 7, and get the product 56. Knowing that this product would have to multiply by 6 and then by 5 and so on, your estimate would probably turn out to be a pretty big number, probably somewhere around 2000.
Now, imagine you’re given a new equation to solve: 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8. Once again, you must conjure up a quick estimate. When faced with this equation, you’re most likely multiplying 1 x 2 = 2, and then 2 x 3, and then realizing that you’re going to continue with a set of relatively small numbers. The weight your mind grants to the bigger numbers, 7 and 8, may not be as heavy as in the last equation since they don’t come first. This time, your final answer will end up reasonably-sized, but not huge: according to several studies, it is likely around 500.
As you’ve probably realized, the two equations given are equivalent, and their real product is actually closer to 40,000 than to either of the numbers projected as your estimates. However, studies show that when given these two equations, people use the first few numbers to estimate their final answer and pay less attention to the later numbers, resulting in hugely different estimates for the two identical equations. In other words, they fall prey to the anchoring bias: allowing the first number they see to cloud their decision-making process.