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 an IMPERIAL BANANA THERMAL DETONATOR - 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, "Charity Drive", 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, and the price "now" (2024) is around 30 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. 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. They speculate that the error in their result is less than 10%, even when their own three predictions (from 120 years to 220 years) differ by over 80%.

To initially mislead the reader and to ultimately demonstrate how easy it is to be fooled by various methods of 'lying with data,' Randall impressively combines several statistical 'sins' in one graph, such as:
* false precision
* extrapolating an order of magnitude deeper into the future than is advisable
* referring to a logarithmic extrapolation as linear
* ignoring historical norms and high variability in making future predictions
* articulating multiple potential scenarios 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 price and 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 an 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. 

(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 log-linear, with price as a logarithmic scale on the vertical (left) axis, which makes it possible to visualize exponential growth as a straight line.)

The accuracy of this prediction depends on these particular extrapolations being valid. The "general inflation rate" line assumes an average rate of around 3%, matching the historic average in the USA. However, assuming a constant inflation rate for the next 200 years is extremely simplistic. Inflation fluctuates quite a lot in response to economic factors and government policies. It was as high as 6% during recent rounds of economic stimulus and caused fears of hyper-inflation. 

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

An additional example of "lying with data" is the use of a logarithmic graph for economic data. It's highly unusual to graph economic data logarithmically, 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 imprecise these extrapolations are.

(The main exception is financial market analysis, in which some traders like to use logarithmic graphs as one of many tools to perceive and predict hidden price trends that don’t show up in normally scaled charts.) 

Another, more subtle, illustration of false precision is the graph's use of three different models 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.

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 -- of 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 threshold), so too is the speaker 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. 

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 economic 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%. (A rare example of a field in which 75-year predictions are highly accurate is demographic age charts, since the number of babies born this year is causal of the # of 75-year-olds alive in 75 years.)

Log scales and their peculiarities are a recurring xkcd theme, and this is the second comic in a row to play with logarithms (the prior one being [[2891: Log Cabin]]). It's also the second comic in the last four to involve predictions across centuries (i.e. [[2889: Greenhouse Effect]]). Another comic whose subject is extrapolation is [[605: Extrapolating]]. This comic looks a lot like [[1007: Sustainable]].

==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]]