How does a median have a value that is a decimal which isn't exactly half of an integer if the data should consist of only integer values?

Question

I real an article which said the average man accumulated 6.1 sexual partners while the average woman accumulates 3.6. If the statistic talked about the average, surely the numbers would be equal-so it must talk about the median. But how is the median 6.1 or 3.6?

http://www.medicaldaily.com/pulse/whats-normal-breast-size-and-penis-size-find-out-if-youre-sexually-average-317324

Answer 1

For most of the reasons mentioned in the Comments, I do not find it remarkable that means would be unequal (except @GerryMyerson 's Comment happens to be explicitly foreclosed by the description in your link). In every survey I have ever seen on the issue of numbers of sexual partners, men report more of them women--even in what appear to be populations for which results should logically be exactly equal. (In this particular case, I hope I can be excused for harboring the suspicion that this survey was conducted more with an eye towards ad sales than careful survey design.)

However, see the answer to recent question 1327801 on this site to see how median values might not be integers or half integers, when approximated from grouped data or a histogram.

Note: On a closely related topic, most software packages agree on how to find the median from original data, but they have very different ways of finding the lower and upper quartiles. These differences become negligible with increasing sample size, but they can be confusing to students trying to reconcile hand computation, answer book values, and values from software. [In R statistical software, typing ? quantile gets you a help page that lists nine different formulas in common use to find quantiles (hence quartiles). The median is the 50th quantile, but the methods mainly agree for medians.]