43% of what? How to tell what total a percentage is out of

A regional newspaper runs this line: "Ciudad Ceiba accounts for 43.5% of thefts from businesses." At a La Ceiba meeting, someone says the chain should stop opening stores there, because it's the most dangerous place.

The number is calculated correctly: of the 5,221 thefts from businesses reported in 2025 across the region's 18 municipalities, 2,272 were in Ciudad Ceiba. The question is whether it says what the people in that meeting think it says.

The denominator tells you who you're talking about

Ciudad Ceiba has 1,420,000 of the region's 3,309,450 residents: 42.9%. That 43.5% of the thefts happen there is almost exactly what you'd expect if a business faced the same risk everywhere. The city has a lot of thefts because it has a lot of people and a lot of businesses.

Every percentage is a division, and the bottom part, the denominator, says which group you're talking about. The same count of thefts divided by two different things answers two different questions:

The first division answers where things happen, and it's useful for deciding where to put resources: if you're sending security guards, almost half the problem is in Ciudad Ceiba. The second answers how common it is for it to happen to someone, and it's what you use to compare places. On the page about rates per 100,000 you'll see that Villa Morena, with only 611 thefts, is where a theft is most common.

Before you use a percentage, finish the sentence out loud: "43.5% of ___." If you can't fill in the blank with a specific group, you don't know yet what the number says.

Flipping the question

There's a trap hiding in the denominator that fools even very experienced people. At La Ceiba, 20 people quit in 2025, and Human Resources reports:

"70% of the people who quit were on the night shift."

It's easy to read that as "70% of the night shift quit." Those are two different questions:

• Of the people who quit, how many were on the night shift? The denominator is the 20 people who quit.
• Of the night shift, how many people quit? The denominator is everyone on the night shift.

The first one, on its own, doesn't tell you whether the night shift has a problem: if 70% of the staff worked nights, it's exactly what you'd expect. For the second one you need to know how many people work each shift. You'll work it out yourself.

If the two questions sound the same to you, ask your Maestro for another example of flipping them.

Try it

This exercise uses pandas, a Python tool for working with tables. The first part of the code builds a small table with the two shifts. The second part already calculates what share of the people who quit came from each shift. The third part should calculate what share of each shift quit, but right now it divides by the number who quit: change the denominator to the personas column (people).

If you're not sure which of the two columns goes in the denominator, ask your Maestro.

With the right denominator, the story changes size: 35% of the night shift quit, and less than 4% of the day shift. The night shift does have a problem, and it's worse than the 70% suggested. This time both readings pointed the same way; often they don't, and the only way to know is to calculate the second one.

This happens all the time in reports and the news: "60% of accidents happened in daylight," "80% of customers who complained bought online." Each one describes a group (the accidents, the people who complained) and says nothing about risk until you flip it and divide by everyone it could have happened to.

If you use an AI to pull these percentages from your own spreadsheets, ask it what you'd ask a person: what did it count, and what did it divide by? The takeaway: a percentage means nothing until you know what total it's out of.