Week 21: Develop an above-average understanding of averages

Averages often become values or ideals, and sometimes, those ideals become sales opportunities. |  Wellcome Collection

Averages often become values or ideals, and sometimes, those ideals become sales opportunities. | Wellcome Collection

Those Girl Scout cookies you ordered in Week 19 have probably arrived, so here’s your friendly reminder that “eating for two” means consuming an extra 340 calories a day during the second trimester. That's about 5 Peanut Butter Patties. Not Tagalongs.

We can take one more math lesson from the girl scouts this week: be suspicious of the averages we see reported in the news.

According to a report in Money magazine, the average girl scout sells 150-200 boxes of cookies each cookie season.

How many girl scouts do you know who sell that many boxes? As a scout who had to make cookie deliveries during upstate New York winters, I can tell you from experience that selling 150 boxes of cookies without adult help is…unlikely.

There are a few ways to find the average number of cookies sold by each scout. You could take the number of boxes sold by scouts and then divide that number by the scouts who sold cookies, which is where the 150-200 boxes-per-scout figure comes from. But the problem with this approach is that there are extreme outliers, like 2017’s highest seller Katie Francis, who has sold over 100,000 boxes in her scouting career.

Let’s say that you have a troop of ten scouts, nine of whom go door-to-door and sell 30 boxes of cookies each. The last scout sends the form into work with her parent and sells 200 boxes. The average number of boxes sold by each scout is 47 boxes, but that average doesn’t accurately describe any of the scouts’ sales.

If you want to know what a typical number of boxes sold is, you’d do better to calculate the median (the middle number) or the mode (the most frequent number). In the case of the troop above, both the median and the mode would be 30, which is a more accurate representation of the typical troop member.

What’s the best way to deal with the averages you read about in the news? Take another lesson from the scouts and “Be prepared.”

1) Understand the news’ definition of “average”

As our cookie-related example demonstrates, there’s more than one way to calculate an average.

Many of the pregnancy and parenting stories you will read use only one type of average (the mean), ignoring other possible types of averages (like median and mode). These averages tend to be stated as plain fact without analysis. The writers including averages in their stories may not even know what type of average they are describing. Rather, they are using the average to set a tone. An average can make a topic sound scary, lending an article weight and seriousness (and possibly clicks and shares).

It’s best to regard “averages,” reported in the news, as measures of news value more than actual risk. Think of Katie Francis’ impressive cookie-selling record and ask yourself whether there may be other outliers, or even groups of outliers, represented in that average. Ask if another way of calculating the average (median, mode) could give you a more accurate representation.

2) If you can’t count it, you can’t average it

Here’s another type of newsworthy average: The average person swallows eight spiders a year during their sleep.

If that statistic is keeping you up at night, looking for outliers probably won’t help much. Depending on how many outliers there were, that might mean one person is eating pounds of spiders and the rest of us are only swallowing one or two. But that’s still one or two spiders(!), so we’re unlikely to feel comforted by the presence of outliers.

In these cases, it’s worth asking where the average came from.

None of us are swallowing any spiders, because that sleep-eating spider claim has been well-debunked. In general, be skeptical of averages that aren’t based on any kind of rigorous counting.

3) Don’t aim for average

We see a virtue in being average. That’s often because, when we’re looking for pregnancy questions, we’re thinking of yet another meaning of average: the “average” pregnancy is the typical one, the safe and uncomplicated one, our desired outcome.

But “average” is a mathematical description that, as we’ve seen above, is only sometimes an accurate reflection of the population at large. Averages can help guide our decision making, but we needn’t look to them as benchmarks.

The average birth weight is 7.7 pounds, but that doesn’t mean there’s anything wrong with a baby who comes in above or below that average.

The average pregnancy lasts 39 weeks, but that doesn’t mean babies born on either side of that date are somehow deficient.

The average duration of first labor is 8 hours, but that doesn’t mean we should panic at 8 hours 1 minute.

In all of these cases, averages provide prospective parents with general sense of what to prepare for, but none should be assumed the right or ideal number.