January 18, 2011

How can I tell if an “average” is a mean or a median?

Q. When reporting on a poll that involves an “average” amount (not just on Pew Research reports, but on all that I have seen), there is seldom any indication of whether the average amount is a mean or a median. Also, no measure of variability is given such as standard deviation or a range. Is there a reason for this? For example, one can statistically compare “65% of voters preferred Candidate X last month, but 62% do this month” (sample sizes are always given). But without a measure of variability, one cannot compare “American white-collar workers spent an average of $9 a day for lunch last month and $8 a day last month.”

Our goal is to make sure that any reference to the average or typical amount also clearly indicates whether a mean or median is being used. But we don’t always achieve that goal. Your question is a good reminder that we should do better. We do make every effort to ensure that we use the most appropriate measure, given the underlying distribution of the variable. We sometimes even report both (for an example, see pages 31-32 of this report (PDF) by the Pew Internet & American Life Project on teens and their mobile phones).

You are correct that we rarely report measures of variability when we report a mean or median. But we are happy to make these available upon request. And more important, we have a standard rule not to state or imply that there are differences between groups or over time unless we have determined that the differences are statistically significant using appropriate tests.

Scott Keeter, Director of Survey Research, Pew Research Center