The Logarithmic Mean for Dummies

formula for logarithmic mean

We say it often enough around Antisocial Network headquarters that we might as well have it tattooed on the forehead of the closest intern: "You don't ask your plumber for medical advice, and you don't ask the grocery clerk how to mortise a hinge." Or something like that; basically, people who know nothing shouldn't be giving advice. That's what we caught today's DotD doing, though... he's Alexander Rudinski, attempting to tell his readers "How to Calculate Logarithmic Mean" for Sciencing.com.

Rudinski's bio says that he has a BS from The University for the Arts (how does an art school give BS degrees?) – a degree in "communications"... Perhaps the lack of of college math¹ hampered his research? Whatever the case, the formula for the logarithmic mean of two numbers, x and y, is

(x - y) / ln(x / y)

That, however, is not what Alexander said. His three erudite-sounding references notwithstanding, it's pretty obvious that Rudinski had no idea what he was writing about. It took him almost 400 words to misinform his reader that the logarithmic mean is, (x - y) / (ln(x) - ln(y)) That's even though the only reference he provided that had the formula in it shows the right formula. Perhaps it was all those Greek letters that confused him: tUA apparently has no fraternities, either...

Whatever the case, Rudinski's example was for the numbers 280 and 190; which – using his incorrect formula – resulted in a final answer of 236.84, slightly higher than the arithmetic average of the two numbers (235). The correct formula yields a value of  232.1 (verified at an online calculator for the topic), which is in line with the Wikipedia article for the topic. That reference states that the logarithmic mean of two numbers is smaller than the arithmetic mean...

That's apparently a check Rudinski never made. Combine that with his failure to transcribe the correct formula and his overly wordy instructions, and Alexander is a prime candidate for Dumbass of the Day.

¹ The school appears to have five science courses (one of which is "Beachcomber Ecology") and one math course... They do, however, have "Travel Course: LA Topics"!

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