Do You Get A Round?

Rounding of numbers has been second nature to all of us since early in our school years. Saying that 96.5517241% of our customers are satisfied is cumbersome if not confusing. Instead we say 96.6% are satisfied or even more simply 97%. It’s such a simple calculation that we do it without a second thought.

99.9% of the time, rounding follows very strict rules. If the part of the number you are “chopping off” starts with five or more you round the last remaining digit up; if it’s less you chop off the unneeded digits and leave the last remaining digit as it is. It would be nice if this simple rule worked 100% of the time, but there is actually a bit more to rounding than meets the eye.

We were taught to always round 5’s up. 2.755 becomes 2.76; 7.5 becomes 8, and so on. For most applications this treatment of 5’s works fine but for some it can introduce a small bias into your findings.

Let’s consider a poll where we ask 200 people how many dogs and cats they own. Suppose the averages are as follows:

Dog – 1.25 per person
Cat – 0.75 per person

In our report, we are rounding everything to one decimal, so we say that people on average own 1.3 dogs and 0.8 cats. The trouble with this is that if we add the two mean scores together, we conclude that the average person owns 2.1 pets (1.3 + 0.8) when in fact they own on average exactly 2 pets (1.25 + 0.75). This is only a small difference, but if we were to expand the study to include rabbits, fish, ferrets, gerbils, guinea pigs, hamsters, and iguanas, there are many more numbers that could potentially land on a five. If we round them all in the same direction, we quickly begin to overstate the average number of pets that people own.

To correct for this bias, when a number ends in five, you should round it up half of the time and round it down the other half. The best way to do this from a mathematical perspective is to randomly round up half of the time and down the other half of the time. Unfortunately, this doesn’t work in practice because each time you calculate a percentage or mean you could be rounding to a different number. 55 out of 200 responses is 27.5%. You can’t call it 27% sometimes and 28% other times. It needs to be one or the other.

The accepted method of rounding fives is to round to the nearest odd number. 27.5% would always get rounded to 27%. 28.5% would always get rounded to 29%. Many research tabulation programs have an option for employing this method of rounding.

Another common mistake of rounding is to round numbers twice. Standard market research data tables typically display percentages to one decimal place. Keep in mind that those numbers are already rounded. If you round them again to whole number percentages in your report, you could be making a mathematical error. Suppose there is a response of 120 out of a base of 320. This evaluates to 36.4741641…%. On a data table, this would round to 36.5%. You might then round that number up to 37%, when in fact the closest integer to the actual percentage is 36%.

Just some little things to keep in mind next time you have data around.