Random sampling” is done by many polling organizations, such as those that conduct political polls. Some people believe that the sample size is small and that it doesn’t reflect the entire population. “If you don’t believe in random sampling, the next time you go to the doctor for a blood test, tell him to take it all” is a response that is popular with pollsters.
 
“If you don’t believe in sampling, be sure—the next time you have a blood test—to get yourself pumped dry…make them take it all!” was said by A. C. Nielsen Jr., president of the ACNielsen global marketing research firm that was founded by his father, in 1967 (although this Google Books date may be incorrect). Two different pollsters used the same joke in 1981 and in 1987.
 
“Whatever you do, always give 100%. Unless you’re donating blood” is another saying involving blood.

 
Wikipedia: Arthur Nielsen
Arthur Charles Nielsen, Sr. (September 5, 1897 – June 1, 1980) was an American market analyst who founded the ACNielsen company.
(...)
Personal life
With his son Arthur Nielsen, Jr., he won the U.S. Father and Son doubles tennis titles in 1946 and 1948.
 
Google Books
TV Guide
1967
Pg. 30:
To those who still harbor reservations, A.C. Nielsen Jr., president of the firm founded by his father, is inclined to quip: “If you don’t believe in sampling, be sure — the next time you have a blood test — to get yourself pumped dry…make them take it all!”
 
6 December 1981, The Chronicle-Telegram (Elyria, OH), “QuoteBag” by Bob Talbert (Knight-Ridder Newspapers), Sunday Scene section, pg. 3, cols. 3-4:
MALCOLM A. McNIVEN, president of the consumer market research division, IMS International: “If you don’t believe in sampling, next time you go to the doctor and he wants some blood, tell him to take it all.”
   
Google Books
Instructor’s Manual
Broadcasting in America:
A Survey of Electronic Media (Fifth Edition)
By Norman Felsenthal
Boston, MA: Houghton Mifflin
1987
Pg. 79:
A humorous way to introduce the principle is to quote A. C. Nielsen, Jr., who said: “Anyone who doesn’t believe in sampling should never have a blood test. The next time you visit the doctor, make him take it all.”
   
20 December 1987, Sunday Intelligencer/Montogmery County Record (Doylestown, PA), “Parade of polls: As the presidential race intensifies, public will be stampeded with surveys” (AP), pg. A-19, col. 2:
Done correctly, the sample can be astonishingly precise. “People have a hard time believing that,” said Harry O’Neill, president of the National Council of Public Polls.
 
“I tell ‘em, if you really don’t believe in sampling, the next time the doctor draws a blood sample, say, ‘No, Doc, take it all.’”
 
ABC News
ABC News’ Guide to Polls & Public Opinion
January 18, 2008
By Gary Langer
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Pollsters have a joke: If you don’t believe in random sampling, next time you go to the doctor for a blood test, have him take it all.
 
Google Books
A Career in Statistics:
Beyond the Numbers
By Gerald J. Hahn and Necip Doganaksoy
Hoboken, NJ: John Wiley & Sons, Inc.
2011
Pg. 222:
If you don’t like sampling, next time you have a blood test, tell them to take it all.
—CBS News (quoted by Katherine Cramer Walsh)
   
AIMRO (Association of Irish Market Research Organisations)
10 QUESTIONS JOURNALISTS SHOULD ASK ABOUT POLL RESULTS
01 February 2011 AIMRO
(...)
This is also well illustrated in a quote made by a famous US market researcher which reads, “If you don’t believe in random sampling, next time you are in for a blood test, ask the doctor to take it all.”
 
Twitter
Barikatul Hikmah
‏@BarikatulHikmah
“Old joke: if you don’t believe in random sampling, next time you have a blood test tell the doctor to take it all.” -@gombang
7:40 AM - 10 Jul 2014