Dr. Deming is often incorrectly quoted as saying: "you can't manage what you can't measure." In fact, he stated one of the seven deadly diseases of management was Running a company on visible figures alone.
In Out of the Crisis, page 121, Dr. Deming states
Deming realized that many important things, that must be managed, cannot be measured. Both those points are important. One, you can't measure everything of importance to management. And two, you must still manage those important things.
The quote from Lloyd S. Nelson, seems to state that most figures are needed, which to me would imply it is possible to get them or the situation is hopeless (if you require something that you can't have in order to succeed then you can't succeed). I believe the quote would be clearer as: "figures on the most important areas of management are unknown or unknowable, and successful managers must nevertheless manage those areas."
The reason Dr. Deming is often misquoted as saying nearly the opposite is likely because he encouraged the use the data when possible. Since failing to use statistical tools to manage was so common, people correctly tied the importance of using data to improve with the Deming management philosophy. However, now many versions on the quote ("you can't manage what you don't measure") is commonly attributed to Deming - incorrectly.
For more on Deming's thoughts on the problems caused by "running a company on visible figures alone (counting the money)" see pages 121-126 of Out of the Crisis.
Dr. Deming is also often quoted as saying: "In God we trust, all others bring data." I believe he did say this, though I don't believe he is the original source (let me know if you have details that would provide more information on this). While this does imply a requirement of data, I believe instead it is meant to encourage people to find a way to get data when possible (it is a memorable quote). If it were not common practice to fail to use data to improve decisions such encouragement would not be needed. However, since we often fail to take steps to take advantage of possible data Deming wished to encourage people to try and use data to improve.
New Economics, page 2:
I believe this adds to an understanding of Deming's thought on the purpose of an organization. Organizations are a means to improve the lives we live.
Dr. W. Edwards Deming management ideas have greatly influenced modern management practice. Many quotes and thoughts are attributed to W. Edwards Deming's system of management. Sometimes these represent his ideas accurately, and sometimes they do not. Here I attempt to clearly indicate what he actual said and include some of my thoughts on what he meant.
Also see: Variation, Management and W. Edwards Deming by Brian Joiner and Marie Gaudard, 1990.Deming on Management