The Percentage Trap: No Base Means Nothing
"Up 100%!" sounds alarming, but if there was only 1 to begin with, a 100% increase just makes it 2.
A percentage detached from its base (how many there were to start) is easy to mislead with. "This drug cuts your risk by 50%"—if the original risk was two in a million, halving it just makes it one in a million, barely any difference to you.
The Average-Number Con: Skewed by a Few
"Our company's average annual salary is 500,000"—sounds wonderful, but it could be the boss alone taking 50 million and the other 99 people each taking a few tens of thousands, all averaged together.
The average is easily pulled off by extreme values and may not represent "what's true for most people." In cases like this, the median (line everyone up and take the person standing right in the middle; with an even number of samples, average the middle two) often tells you more.
Scary Charts: The Truncated Axis
Charts can fool you too. The most common trick is an axis that doesn't start at 0: draw the vertical axis from 98 to 100, and what's really only a gap of 2 makes the bars look worlds apart.
(A non-zero start isn't a con in itself—a zoomed-in view often needs one; what matters is whether it's done deliberately to blow up a meaningless gap.)
With the same data, draw the vertical axis from 0 and the gap is almost invisible; draw it from 98 and it looks several times bigger. The numbers didn't change—how scary it looks comes entirely from how it's drawn.
自测 · 学完检查一下
想真正动手做题、记进度、攒连胜？到互动课里练。
An ad says "this supplement cuts your risk of illness by 50%." To judge whether this is worth caring about, what should you ask first?
答案：What the original risk of illness (the base) was
"Cuts by 50%" is a relative figure, and without the base you can't judge what it means. If the original risk was tiny, halving it makes almost no difference. The other options have nothing to do with the data's real meaning.
A small team has an "average monthly salary of 60,000," but most people actually earn just over 10,000. What's the most likely reason?
答案：A tiny number of people earn extremely high salaries, pulling the average up
The average is pulled off by extreme high values, so it sits above what most people really earn. Here the median better represents the majority, so the second and third are wrong.
True or false: if a bar chart's vertical axis doesn't start at 0, it can make a very small gap look enormous.
答案：True
Truncating the vertical axis (not starting at 0) is a common trick for exaggerating gaps—the data is unchanged but the visual impact is magnified. When reading a chart, check the axis starting point first.
True or false: "sales grew 200%" must mean a lot was sold, because the percentage is so high.
答案：False
A 200% increase is relative to the original base. If only 2 were sold originally, a 200% increase is just 6. A percentage detached from its base says nothing about the absolute scale.
When a dataset has extreme values that skew the average, the value you get by lining up all the data and taking the one right in the middle is called the ____, and it often better represents most people.
答案：median
After sorting, the value right in the middle is the median. Unlike the average, it isn't easily skewed by extreme values, so it better reflects the reality for most people.
Faced with a line chart that makes you "feel an explosive surge at a glance," what's the best first step?
答案：Check where the vertical axis starts and whether the scale is even
Check the axis starting point and scale first to tell whether the steepness is a real trend or an illusion created by how it's drawn. Believing a steep curve outright is exactly what the chart wants; color and the poster don't determine whether the data is true.