50% of what?
A percentage can be perfectly correct and still leave out the number you need.
Suppose an event happens twice in every hundred cases. After a change, it happens once in every hundred. The rate has fallen by half: a 50% relative reduction. It has also fallen from 2% to 1%: a reduction of one percentage point.
These are illustrative numbers, not the results of a study. Both descriptions of the change are correct. A reader who sees only “50% lower” cannot tell what the starting rate was.
Put the starting number back.
Before repeating a percentage, find the original value, the new value and the group being counted. Check that the comparison covers the same period and uses the same definition.
For our example, a useful sentence would be: “The rate fell from 2 in 100 to 1 in 100, a 50% relative reduction.” The reader can now see the size of the change as well as its proportion.
To calculate the relative reduction, divide the drop by the original value: (2 − 1) ÷ 2 = 0.5, or 50%. To calculate the percentage-point change, subtract the rates: 2% − 1% = 1 percentage point.
Ask which average.
A similar problem turns up with averages. Take five values: 10, 10, 10, 10 and 60. Their mean is 20. Their median, the middle value once the values are ordered, is 10.
The mean has not made a mistake. It has answered a particular question. If the article means to describe a typical observation, the distribution and choice of measure deserve attention.
A mean, a median and a carefully chosen range can each be useful. Decide which matches the question being asked, and name it in the copy.
Leave enough for the next reader.
Keep the original table or passage, its source link, the period and the definitions beside your note. If the source gives uncertainty, a range or a restriction, keep that too.
Our free source-note worksheet gives you somewhere to record the claim and the passage you checked. It works without an account or another subscription. Save the downloaded note before closing the page.
Verity is fact-checking software for checking claims and reviewing their sources. These arithmetic examples explain a reading habit; they are not a product-accuracy result or a promise that software will settle every numerical claim.