Editing 2892: Banana Prices

{{comic
| number    = 2892
| date      = February 9, 2024
| title     = Banana Prices
| image     = banana_prices_2x.png
| imagesize = 564x378px
| noexpand  = true
| titletext = It's a linear extrapolation, Michael. How big could the error be? 10%?
}}

==Explanation==
{{incomplete|Created by a REPUBLIC BANANA PHONE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

[https://www.youtube.com/watch?v=Nl_Qyk9DSUw ‘It’s one banana, Michael. What could it cost, $10?'] is a line from an {{w|Arrested Development}} episode (Season 1, Episode 6, "Visiting Ours", 2003) that became well known as a meme used to mock out-of-touch elites. The character who spoke this line -- Lucille Bluth, a rich socialite -- didn't know whether a banana cost $10 in 2003 because she never did any grocery shopping "because we have people for that."  According to the graph, the banana price at the time of that episode was actually just under 25 cents.

'''This comic illustrates a whole suite of ways to violate statistical best practices and to 'lie with data.' And the additional use of an "unreliable narrator" device gives this comic several layers of meaning.'''

To initially mislead the reader and to demonstrate how easy it is to be fooled by various methods of 'lying with data,' Randall illustrates several statisical 'sins,' such as:
* simplistic extrapolation and false precision
* ignoring historical norms in making future predictions
* logarithmic scales when they're inappropriate
* developing multiple scnearios that are actually highly correlated with each other.

At first, the comic looks like a wry observation that the irony of this sitcom line will be obsolete in a century or two. This comic shows a graph of three different projected future prices for bananas over the next 250 years. One extrapolates from the current inflation rate in general. Another uses the more specific inflation rate for fresh fruit, which is made from less data but is more relevant than a general rate dominated by the cost of housing. The final line is a "linear" extrapolation from 50 years of historic banana prices. The comic seems to say that it will take a century or two before the irony of the sitcom quote becomes anachronistically meaningless. This prediction depends on these particular extrapolations being accurate.

(While these extrapolations look linear, they are in fact logarithmic, since a linear extrapolation on a graph with a logarithmic scale is actually a logarithmic extrapolation. The graph is drawn to a logarithmic vertical scale on the vertical (left) axis, which makes it possible to visualize exponential price-rise as the dotted line.)

Upon closer inspection though, it's apparent that the graph-maker-cum-caption-writer is making some absurd assumptions about inflation continuing at its current level of about 3%. The caption writer, in this case, is an unreliable narrator who is ''also'' humorously out-of-touch like Lucille Bluth, but in a different way. If inflation returns to its recent historic norm of 2%, then it will actually take 200 years for the price of a banana to rise past $10. But as recently as 2022 the rate of inflation was as high as 6% in the US, a rate at which the banana would reach $10 in a mere 60 years. Even a short period of high inflation would be equivalent to a long period of low inflation. Simply assuming a constant 3% inflation rate for the next 100 years -- despite historical evidence -- is extremely simplistic.

Another more subtle illustration of false precision is the graph's use of three different assumptions for the extrapolation of banana prices. At first glance, using three different trend lines seems to show a "range" of potential scenarios and acknowledge the prediction's uncertainty. However, all three underlying trends are correlated: general inflation is highly correlated to fruit price inflation and banana price inflation. Using three different trends that are all highly correlated is scant better than using just one.

An additional example of "lying with data" is the use of a logorithmic graph for economic data. It's highly ususual to graph economic data logorithmically, as economic variables rarely show exponential change over time -- and even when they do, it's easier to show that change on a normal linear graph. If this same set of extrapolations were shown on a linear graph, the absurdly accelerating slope of the extrapolations would give away how rediculous these extrapolations are.

Finally, the reference to "BLS/St. Louis Fred" -- a widely-respected source of economic data -- appears to lend credibility to the graph, but the only data that is truly credible is the historic price data. It's one more example -- citing respected sources -- as a way to fool unsuspecting readers into giving a prediction more credibility than it deserves.

The title text is a wink from Randall about this unreliable narrator by using the ignorant tone of Lucille Bluth to wryly acknowledge that, in fact, that error of the extrapolations greatly exceeds 10%. Just as Lucille was very wrong about a $10 banana (a price threashold), so too is the Lucille of the title text very wrong about the 10% error (a proportional change). It does so in the form of a meta-joke about the false precision of extrapolations, while continuing the theme of the speaker's extreme ignorance. Assuming that the error couldn't be more than 10% shows that the Lucille speaker continues to be hilariously off-base, presuming far more accuracy from a multi-century prediction than is warranted.

Besides the inflation example, another way the extrapolation could be wrong was if -- in the next 100 years -- there was a massive banana crash or extinction {{w|Banana#Pests, diseases, and natural disasters|as has happened}} {{w|Gros Michel banana|before}} due to banana's lack of genetic diversity, in which case the sharply reduced supply of bananas could send the price past $10 very quickly. 

Overall, the comic is a clever commentary about the false precision of extrapolation and how easy it is to be fooled by it, illustrating its point by initially misleading the reader with its own false precision, and wrapping it all in a pop-culture reference. Any extrapolation into the distant future based on past data points is just an educated guess likely to be quite wrong, with an expected error far in excess of 10%. 

Log scales are a recurring xkcd theme, and this is the second comic in a row to involve logarithms (the prior one being [[2891: Log Cabin]]). It's also the second comic in the last four to involve prediction across centuries (i.e. [[2889: Greenhouse Effect]]).

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A graph with the x-axis showing time, from the years 1950 to around 2275. The y-axis is a log scale showing the price of a banana from $0.10 to over $10.00. A label called "Price of a banana (BLS/St. Louis ''Fred''[https://fred.stlouisfed.org/])" show a rising trend in the price of a banana. There are two dots on that trend. One is labeled "Episode airs" and the other one "Now". 3 extrapolations shown as dashed lines labeled "General inflation rate", "Fresh fruit price trend" and "Banana price trend" extend until reaching the $10 mark, indicated by 3 dots.]

:[Caption above the graph:] "It's one banana, Michael. What could it cost? $10?

:[Caption below the panel:] That line probably has another century or so left.

{{comic discussion}}

[[Category:Line graphs]]
[[Category:Timelines]]
[[Category:Fiction]]
[[Category:Extrapolation]]