Misleading axes

Births rose 10.6% from 2023 to 2025, but on a bar chart whose axis starts at 220 thousand the 2025 bar is drawn 3.43 times as tall.

Every chart involves choices, and some choices change the message more than the data do. The most common one is where the vertical axis starts. On a bar chart, starting the axis above zero cuts off the bottom of every bar, and since the bars are read by their length, the remaining stubs exaggerate every difference. OpenStax lists it among the ways a chart can mislead and adds that, if the axis began at zero, the manipulation would be obvious.

Computing the illusion

Korea recorded 230.0 thousand births in 2023 and 254.3 thousand in 2025. The real ratio is 254.3 ÷ 230.0 ≈ 1.106, an increase of about 10.6%. Now start the axis at 220. The 2025 bar is drawn from 220 to 254.3, a length of 34.3, and the 2023 bar from 220 to 230.0, a length of 10.0. On the page the 2025 bar is 34.3 ÷ 10.0 = 3.43 times as tall. Start the axis at 225 and the drawn ratio becomes 29.3 ÷ 5.0 ≈ 5.86. The data have not changed at all; only the cut has.

The general rule follows from that example. If the axis starts at b, a bar for value v is drawn with length v − b, so the drawn ratio of two bars is (big − b) ÷ (small − b). When b is 0 this equals the real ratio big ÷ small. As b climbs toward the smaller value, the denominator shrinks toward zero and the drawn ratio grows without limit.

Are line graphs different?

A line graph is read by the position of its points and the slope between them, not by the length of anything, so it may start its axis above zero. A fertility rate that moves between 0.72 and 1.24 would be a nearly flat line on an axis from 0 to 5. Statisticians accept a non-zero line axis as long as it is clearly labelled. The cost is that the steepness then depends on the chosen range, so read the numbers on the axis before you judge how dramatic a change is.

Other ways to bend a picture

OpenStax lists more. Stretch the time axis and a volatile series looks calm; squeeze it and any growth looks explosive. Report a value in small units, such as won instead of billions of won, and every change looks large. Average daily data into quarters and the swings disappear. On a histogram, make one class wider than the rest and its larger area suggests a larger share. None of these needs a false number. The defence is the same each time: read the axes, the units and the intervals, and recompute the comparison yourself.