Question
Ask what the percentage is a percentage of
A percentage without its whole is an unfinished sentence.
When it fits
- A report makes a claim such as '80% agree' without making the group obvious.
When to avoid it
- A clearly stated denominator does not remove nonresponse or selection bias.
A question to ask
Who or what was eligible to enter the denominator? · Who actually appears in it, and who is missing? · Does the conclusion refer to that same group?
Why it matters
Identify the numerator, denominator and inclusion rule before interpreting the number. Eighty percent of respondents is not necessarily eighty percent of customers. The arithmetic can be correct while the sentence quietly changes the population it describes.
An example
Eight positive replies from ten replies do not establish satisfaction among all two hundred invited customers.
Check your result
You can complete the sentence with the actual counted group and period.
Keep this limit in mind
- A clearly stated denominator does not remove nonresponse or selection bias.
Connected ideas
Useful withSeparate percentage points from percentage change
Evidence and sources
A percentage expresses a quantity relative to a specified whole, with 100 as the reference scale.
The definition cannot establish whether the chosen whole represents the relevant population.
Prealgebra 2e, 6.1: Understand Percent · Definition of percent