📊 Data
📉When Averages Mislead
Average salaries that look too high, review scores that look too good — computing an average is step one, spotting its misuse is the real skill.
"The average monthly salary at our company is 7,600 yuan!" the job ad boasts — yet once inside, you learn that nine coworkers each earn 4,000. The average was computed correctly; it was simply dragged away by one person. Knowing how to compute mean, median and mode is only the beginning. This lesson is about how those three numbers get misused — and how to see through it.
One executive lifts the whole company
Nine employees earn 4,000 a month and one manager earns 40,000. The mean: — ninety percent more than what the nine people actually make. The median needs only a quick sort: 4,000, not budged an inch.
Extreme values pull the mean around while the median stands firm. So when a headline says "average income", ask first: does that mean the mean or the median? Let one or two extreme values slip into the crowd and the portrait of the "typical person" comes out warped. How pay should be read gets its own treatment in the lesson on wages.
The survivors: data that never speaks
During World War II, the military wanted to add armor to bombers. Counting bullet holes on the planes that returned: wings riddled, engines nearly untouched. Some suggested armoring wherever the holes were densest — but the statistician Abraham Wald said the opposite: armor the engines.
The reason hides in the planes that never came back. A bomber shot in the wings could often limp home; one shot in the engine usually went down. The data you counted came only from survivors, and survivors never speak for the whole. Online review scores play the same trick: dissatisfied customers mostly just leave without writing anything — a high rating may only mean the complaints had nowhere to go.
Which representative fits the job
Back to the division of labor among the three averages. A shoe store stocks by the mode — whatever size sells most is what to order; the average shoe size helps nobody. House prices and incomes call for the median — so mansions and bosses cannot fling the number into the air. When the data cluster together with no outliers, the mean is the most natural choice, as with the heights of a class. Which number to pick depends on the question you want answered.
The digits themselves may be honest and the presentation still deceptive — chopped axes and cherry-picked time ranges are classic moves covered in misleading graphs. And one step further upstream: if the sampling itself is biased (questionnaires handed out only at the gym door), the data arrive crooked — see surveys and sampling.
The data lab
Count
7
Mean
6.14
Median
6
Mode
8
Add a 20 to the default dataset (the largest value the input box allows): the mean leaps from about 6.1 to about 7.9, the median slides only from 6 to 7, and the mode 8 stays put. Delete it and everything snaps back. Pulling that lever once by hand beats reciting "outliers affect the mean" ten times.
Check yourself
Quick quiz
1. Nine people earn 4,000 a month and one person earns 40,000. What are the mean and the median?
2. Returning bombers have the most bullet holes in their wings. Where should the armor go first?
3. A shoe store manager is deciding which sizes to stock. Which average matters most?