Ask five builders what a job costs and you get five estimates of one number. They differ because estimating is hard, not because the job has five prices. Take the lowest and you have not found the cheapest builder — you have found whoever's estimate came out lowest, which is a different thing and is systematically below what the job costs.
That gap is not an opinion. For n estimates with spread σ around a common centre, the lowest lands about a(n)·σ below the centre, where a(n) is the expected value of the minimum of n standard normals:
n 2 3 4 5 6 8 10
a(n) 0.56 0.85 1.03 1.16 1.27 1.42 1.54
Which has a consequence nobody likes: more bidders means a lower winning bid and a bigger expected shortfall. The extra bidder did not make anybody cheaper. It gave the minimum another chance to be wrong.
None of this says the low bidder is wrong. It says what to hold back.
Nothing is uploaded and nothing is stored. Tender prices are commercially sensitive and this page has no server to send them to — the arithmetic runs in your browser and its own policy forbids it from talking to anything.
Your quotes
What another bidder costs you
Hold the spread still and grow the field. Nobody's costs change, and the expected winning bid falls anyway — because the minimum of six numbers is further below the middle than the minimum of five. This is the table that makes “get another quote” stop sounding like free money.
What it does not know
It assumes the quotes are for the same job. They usually are not, quite: different exclusions, different provisional sums, different allowances for the thing nobody has opened up yet. Half of what looks like a spread in estimating skill is a spread in what was priced, and this page cannot see any of it.
It assumes the estimates are honest attempts. A bid priced to buy the job and win it back on variations is not an estimate of anything, and it looks exactly like a good estimate that came out low. The arithmetic here cannot tell those apart, and neither can a spreadsheet — only the scope conversation can.
The spread comes from three to six numbers. Every figure on this page is proportional to it, and a spread measured from four quotes is itself a rough thing. The correction for that bias is applied and is exact; the estimate underneath it is still four numbers.
It assumes the estimates are spread symmetrically. Construction estimates are not, quite — the tail of nasty surprises is longer than the tail of pleasant ones, which makes the shortfall here an understatement rather than an overstatement.
Cheapest is not the same question as best value. Programme, defects, whether they turn up: none of that is a number on this page, and all of it costs more than the gaps here when it goes wrong.