## Magnitude and Precision September 14, 2009

Posted by Chuck Musciano in Leadership.
Tags: , ,

A quick math test:

Paula Programmer has been assigned to write a new interface for a web-based application.  She estimates that the task will take seven days.  After one day of hard work, how much of the task has Paula completed?

2. 14%
3. 14.28571%
4. Not enough information to answer.

Optimists might answer A, on the assumption that Paula estimates well and works consistently.  Pessimists will always answer D, believing that until Paula delivers some code that works, she’s done nothing but shop on eBay all day. An optimist that can do math in their head might come up with B.  Finally, a compulsive optimist with a calculator will answer C.

Why?  Why are people instinctively drawn to numbers with more digits?

I’ll tell you why: more digits imply more precision.  Many years ago, right around the time that schools stopped teaching kids how to use slide rules, they stopped teaching kids the difference between magnitude and precision.  Instead, armed with calculators, kids can rattle off an answer to 8 digits, blissfully unaware that digits 2 through 7 are meaningless.

To review: the result of any computation is only as accurate as the least accurate of all the values used in the computation.  If you divide a one-digit number by another one-digit number, your answer is accurate to a single digit.  In Paula’s case, when you divide “about a day” by “about seven days,” you get A, “about one-seventh,” her inline shopping habits notwithstanding.

Why does this matter?  We deal with numbers all the time in our jobs.  As leaders, we constantly request estimates from our people, and ask them to compute cost ratios, return on investment, completion percentages, and the like.  The resulting numbers are often used to justify projects, allocate resources, and make important business decisions.  Often, the false precision in these numbers gives them a credibility they do not deserve, and our decisions suffer as a result.

Just as distressingly, people often do a lot of extra work to create precision where it isn’t needed.  That extra precision doesn’t help, and the time wasted making the number that accurate can’t be recovered.  I sometimes ask for numbers “to the nearest x zeroes” so that my people know not to waste their time creating useless precision.  Thus, a request “to the nearest four zeroes” should be rounded to the nearest \$10,000, and so forth.  They save time, I get the answer I need, and we all move forward.

Given that the public school system long ago ceded their responsibility for effective mathematics education, we must take on that task.  Effective delegation includes expectation management, and that includes defining the precision of any numerical results we request.  Make sure your people know what you want and how precise you want it.  You will get better answers and they’ll save time.  My estimate? At least 4.32675%.  Maybe more!

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