Bernoulli, Bearnaise, and Statistics for Lawyers

I’m no statistician, but I do like mathematics, statistics, and quantitative methods in general.  That’s why I hate to see lawyers use confusing language when writing or talking about these subjects.  Take this recent quote from an article on the US News website about lawyer salaries.  Here’s the part that’s troublesome (emphasis added):

Law school graduates “can expect a starting salary in the range of anywhere from a low of $50,000 all the way up to $205,000, and those are median salaries,” says NALP executive director Nikia Gray.

Is that wrong?  I’m not talking about merely being misleading.  That's another matter entirely, as only the very top students at the most “prestigious” law schools will have a realistic chance of making a $205,000 salary upon graduating and passing the bar.  Rather, I'm wondering if that quote is wrong.  Here’s what I mean:

While I suppose it’s possible to give a “range” of “medians,” that doesn't seem to make much sense.  A range, with a high and low number, is self explanatory.  The median would be the midpoint in that set of numbers.  Is the article confusing two things?  To make matters worse, in another part of the article it refers to a single number, $50,000, as a "range."  And returning to the $205,000 as the highest median—in a range of medians?—nowhere does the graph in the article show such a median for any sized firm, or for all firms overall.  Color me confused.

Statistics can be complex, and require precision of language.  (For an example of real complexity, and my best attempt at using precise language to match, see footnote 144 of this article.)  Nonetheless, the median can be a great statistic.  It is often far more valuable than the mean (average).  For example, consider the fictional law school, Legal Watchdog University, that had five graduates in 2023, all of whom got jobs that paid as follows:

1. $205,000
2. $50,000
3. $50,000
4. $50,000
5. $50,000

The average of these five is $81,000.  But that figure is skewed by the one guy or gal that made $205,000—possibly because their father or mother was a partner at a big law firm and dutifully got them hired.  Unless a prospective student of Legal Watchdog U. has a similar familial connection, he or she can’t expect to make $205k—or even the average of $81k, which no one is making!  Rather, the median, a $50,000 starting salary, is a much more useful statistic for would-be students to ponder before enrolling and paying the Legal Watchdog U. its $49,999 in annual tuition (plus room, board, books, and living expenses).

And, while on the topic of statistics, remember not to confuse Bernoulli with Bearnaise.  It’s a very important distinction when crunching numbers, eating out at a fine restaurant, or hitting on your statistics professor:

Hat tip to Attorney Mo Hernandez for the link to the above US News article.