The first number you see changes how you perceive everything that comes after.
Without a reference number, we don't know whether a price or a quantity is high or low, so we anchor on the first one available to judge it, even if it's arbitrary. That's anchoring bias.
In a now-classic study, people were asked to spin a rigged wheel (which could only land on 10 or 65) before estimating what percentage of African countries belong to the UN. The average answer from the group that saw the wheel land on 10 was much lower than the group that saw it land on 65, even though the number had no real connection to the question.
In a real project for an insurance company, the lack of a similar anchor was exactly one of the main barriers to selling a $10-a-month children's health insurance plan. Customers had nothing to compare the price against to decide whether it was fair.
When estimating an unknown value, we adjust from the first number available instead of starting from zero, and that adjustment is almost always insufficient. The anchor stays fixed in the mind even when we know it has no bearing on the correct answer.
Source: Tversky, A. & Kahneman, D. (1974). Judgment Under Uncertainty: Heuristics and Biases. Science, 185(4157), 1124-1131.
Anchoring shows up in any negotiation or pricing decision without an explicit point of comparison, which is common in markets with no public list price or reference price. Showing a "before" price next to the real one, or comparing against the cost of not solving the problem, are simple ways to set an anchor in your favor instead of leaving it to chance.
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