The pundits and the rounding error

HRC is leading Obama by about 9.4 percentage points in Pennsylvania. But by rounding her 54.7% up to 55%, and his 45.3% down to 45%, the media transform a single-digit victory into a double-digit victory. (I estimate that the actual final margin will be 9.1%, which will STILL be rounded up to 10%.)
Always round after you calculate, not before.

Look around the web, and you’ll see lots of discussion of Hillary Rodham Clinton’s “10-point win” over Barack Obama.

I think it was my sixth-grade teacher who told me always to round after the calculation rather than rounding the inputs to the calculation. Too bad she doesn’t work for any of the big media outfits.

According to CNN, Clinton has 1,258,000 of 2,300,000 votes. That comes to just under 54.7%, which means that she beat Obama by 54.7 – 45.3 = 9.4 percentage points. If you weren’t interested in too much precision, you might round it down to 9 points.

But instead, CNN rounds 54.7% up to 55%, and 45.3% down to 45%, giving Clinton an apparent 10-point win. Everyone else does the same.

And that will still be apparently true even if, as I estimate, the final margin after those last Delaware County and Philadelphia precincts come in is 54.5+ to 45.4+.

So a margin of about 9.1 points gets translated into a margin of 10 points: a single-digit win into double-digit win. And all because the networks don’t think their viewers can stand three significant figures, and the pundits can’t be bothered to do their own arithmetic.

Update A reader points out that the rule “calculate, then round off” applies only when you’re rounding off just to save space. If the rounding reflects the limits of precision of the underlying measurements, it’s better to get rid of the noise first.

Author: Mark Kleiman

Professor of Public Policy at the NYU Marron Institute for Urban Management and editor of the Journal of Drug Policy Analysis. Teaches about the methods of policy analysis about drug abuse control and crime control policy, working out the implications of two principles: that swift and certain sanctions don't have to be severe to be effective, and that well-designed threats usually don't have to be carried out. Books: Drugs and Drug Policy: What Everyone Needs to Know (with Jonathan Caulkins and Angela Hawken) When Brute Force Fails: How to Have Less Crime and Less Punishment (Princeton, 2009; named one of the "books of the year" by The Economist Against Excess: Drug Policy for Results (Basic, 1993) Marijuana: Costs of Abuse, Costs of Control (Greenwood, 1989) UCLA Homepage Curriculum Vitae Contact: