There is a penalty for ignorance. We are paying through the nose.

Quote from W. Edwards Deming:
There is a penalty for ignorance. We are paying through the nose.

無知（不懂得系統合作雙贏、變異、控【管】制圖原理…….）要付出昂貴的代價的……
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penal (CAUSING DISADVANTAGE)
adjective UK
having a harmful effect; causing disadvantage:
They complained about the penal and counter-productive tax rates.
Employees regarded the childcare charges as penal.

penalty noun [C]
Loss of privacy is one of the penalties (= disadvantages) of success.
She has paid a heavy penalty (= suffered serious disadvantages) for speaking the truth.

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pay through the nose INFORMAL
to pay too much money for something:
We paid through the nose to get the car fixed and it still doesn't go properly.

(from Cambridge Advanced Learner's Dictionary)
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pay through the nose
Pay an excessive amount for something, as in We paid through the nose for that vacation. The origin of this term has been lost. Possibly it alludes to the Danish nose tax, imposed in Ireland in the 9th century, whereby delinquent taxpayers were punished by having their noses slit. [Second half of 1600s] To pay through the nose就是用高價買一樣東西，往往要比原來的價值高很多。像普通店裡一件襯衣要40美元，在他們這裡就要200美元。 .
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There are a couple of competing folk derivations of this phrase, but they are regarded by philologists as somewhat far-fetched.

One derivation holds that it is a reference to the Danish poll tax on the Irish in the ninth century. The story goes that the Danes slit the noses of non-payers. However the phrase did not appear in print until 1672.

Annother possible explanation is placed on Viking raiders. Vikings would require the payment of tribute from cities they did not raid. If the king refused to pay tribute they would slit their noses. Hence, the king paid "through" the nose.

Another explanation relies on the use of rhino as a slang for money. Rhinos is the Greek word for nose, thus a rather loose connection is supposed to be set up between paying and noses. A nosebleed as a metaphor for being "bled dry" of money.

In sixteenth century English, Italian, Greek and Latin, however, there is found an already well established expression "to lead by the nose," which means to force or control someone's actions as a farmer would lead a bull by a ring through its nose. It also has connotations of making a fool of someone. ( 'led by the nose, as asses are' (Othello, Act I, Sc 3). Thus to pay through the nose could have originated as an extension of this to denote payment for something at a premium because of lack of alternative options.
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（「美國習慣用語」第十二講- 簡 HC已改正Dutch）
常用的習慣用語: Pay through the nose。

pay through the nose的確切意思是付出比真正的價值高得多的錢，或者說付出的錢實在太多而感到心痛。

我們來舉個例子吧：
例句-3: "My brother Bob borrowed the money to open his restaurant five years ago when the interest rate was so high, so he's been paying through the nose ever since."

這個人說：“我哥哥在五年前借錢開他那個飯館的時候正好利率非常高。所以,他從那時起就一直在大筆大筆地還債。”

這樣由於利息高而付許多錢來還債當然誰也不願意。可是,也有人心甘情願出高價來買那些他們認為值得買的東西。下面一個例子就可以說明這一點：
例句-4: "Life is funny. When the famous Dutch painter Vincent Van Gogh was alive, nobody wanted to buy his pictures. But now rich people will pay through the nose for one, sometimes more than five million dollars."

這句話的意思是：“人生實在是很有趣的。當那位有名的荷蘭畫家凡高還活著的時候，沒有人要買他的畫。可是，現在那些有錢人卻願意出高價買他的畫，有時候一張畫就要五百多萬美元。”