Math with Bad DrawingsCartoon Archive

Which "Mean" Do You Mean?

August 6, 2024Original blog post

Eight kinds of 'mean,' from the real arithmetic, geometric and harmonic means to joke means like the slothometric, FOMO-metric and résumétric.

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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.

Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2024-08-06-which-mean-do-you-mean/ (CC BY-NC 4.0)
Transcript

[1] Arithmetic Mean: sum of data, divided by n. [One person with all the cookies] "Worry not, friends! We have, on average, two cookies each."

[2] Geometric Mean: product of data, to the nth root. A: "Wait, we lost 28%… then we gained 28%… and somehow that's an average loss of 4%?" B: "Sure, the mean of 1.28 and 0.72 is 0.96. Everyone knows that."

[3] Harmonic Mean: n over sum of reciprocals of data. A: "How fast did you run?" B: "Half a mile at 15.5 mph, then I got tired and did half a mile at 0.5 mph… so on average, 8 mph. Not bad!" A: "So why'd a 1-mile run take you over an hour?" B: "Oh, you want the *harmonic* mean? Weird flex, but okay."

[4] Slothometric Mean: one data point, treated as universal. A: "Sorry, people don't care for radishes." B: "Based on actual data? Or are you just extrapolating from your own preference?" A: "My preference *is* data."

[5] Politicometric Mean: a fancy way of saying "median." [Signs: "EAT THE RICH" · "LET THE RICH EAT US"; in the middle, the MEAN VOTER: "anyone know where I can get a soft pretzel?"]

[6] FOMO-metric Mean: sum of the data, divided by the number of data points NOT included. A: "Wow, your Instagram makes your average day look magical." B: "But everybody else's makes my average day look like bread mold."

[7] Resumétric Mean: sum of your data, plus other people's data, plus maybe a little more data you invented, divided by n. [Résumé: "As project manager, I was responsible for several projects → thousands of projects → works such as gods envy and men worship in terror"]

[8] Vaguemetric Mean: some of the data, divided by "eh." A: "Come join us in the multilevel marketing of pyramids!" B: "How many pyramids does the average person sell?" A: "Thousands!" Pyramid: "Yes, zero thousands."

Topics
Statistics › MeanStatistics › Measures of CenterStatistics › Geometric MeanStatistics › Harmonic MeanStatistics › MedianStatistics › Sampling › Sample SizeNumber & Arithmetic › PercentsNumber & Arithmetic › Rates › Speed
Level
Middle SchoolHigh SchoolAP StatisticsCollege
Themes
FoodMoney & ShoppingWork & JobsPoliticsTechnology