# Innumeracy in public media today

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• phinds
phinds
Gold Member
TL;DR Summary
CNN makes a blatant math error
I OFTEN see ridiculous math statements in the public media, usually limited to such publications as Time Magazine and others of that ilk, and even more so on the Internet, but occasionally even in more serious media such as the NASA web site and The Economist. Just ran across another one on the CNN news web site.

Caitlin Clark is set to make $78,000 salary as the WNBA's number 1 overall pick, which is about 137% less than the NBA's number 1 overall pick who will earn$10.5M.

Now, I get that her salary is about 93% of his (which I think is fair to interpret as 93% lower than his), not 137%, but I'm curious how anyone could even GET 137%. I mean, math innumeracy is common but how do you get such a ridiculous answer? I can't think of any computation that could result in anything like that, can you?

What they meant was that his salary is approx 137 times larger than hers. 137 being, of course, the fine structure constant!

Klystron, russ_watters, Vanadium 50 and 3 others
78000/10.5m ##\approx## 0.7%, isn't it? So 99.3% lower? Or am I misunderstanding the numbers?

10.5m is also 135 times 78000, which is somewhere near 137, if nowhere near 137%.

Mark44 and Hornbein
What's worse than the innumeracy is how proud they all are of it!

PeroK said:
What they meant was that his salary is approx 137 times larger than hers. 137 being, of course, the fine structure constant!
Nice try, but that would actually give that his salary is 1,346% greater than hers.

Ibix said:
78000/10.5m ##\approx## 0.7%, isn't it? So 99.3% lower? Or am I misunderstanding the numbers?
I slipped a decimal point. You are correct. See, I'm allowed math innumeracy also

Ibix
Ibix said:
10.5m is also 135 times 78000, which is somewhere near 137, if nowhere near 137%.
Good point. Maybe that's how they got it.

phinds said:
Nice try, but that would actually give that his salary is 1,346% greater than hers.

A percentage difference only really makes sense when the difference is relatively small. In this case, her salary is about 0.7% of his. It's unusual to say that his salary is 13,500% more than hers. That's not a case where a percentage makes much sense, compared to simply saying 135 times greater.

symbolipoint, phinds and OmCheeto
PeroK said:
A percentage difference only really makes sense when the difference is relatively small. In this case, her salary is about 0.7% of his. It's unusual to say that his salary is 13,500% more than hers. That's not a case where a percentage makes much sense, compared to simply saying 135 times greater.
I agree

I still remember from over a decade ago "The Antarctic peninsula has been warming over the last decade by 32.1 F per year."

By now it is surely hotter than Venus.

JoseRomero and phinds
Ibix said:
78000/10.5m ##\approx## 0.7%, isn't it? So 99.3% lower? Or am I misunderstanding the numbers?

10.5m is also 135 times 78000, which is somewhere near 137, if nowhere near 137%.
Actually his salary is 13362% greater than hers. The math of percentages is weird and tricky. If X's salary is double of Y's, then X's is 100% higher. If the ratio is 134 then the percentage is 13300%. Doing decreases is even more weird.

I have seen math mistakes in The Economist and New York Times long ago. They both published graphs that contradicted their conclusions. More recently I saw a percentages mistake from the World Bank. https://science1arts2and3politics.substack.com/p/world-bank-gets-the-math-wrong
Like I said, percentage math is tricky.

It has been my observation that the median person is completely innumerate. Concepts like an average mean nothing to them. I often see absurd economic/political uses of numbers be widely accepted and never questioned. I wonder whether the writers really believed in what they were saying or were cynically taking advantage of the dominance of innumeracy.

phinds
Hornbein said:
It has been my observation that the median person is completely innumerate. Concepts like an average mean nothing to them. I often see absurd economic/political uses of numbers be widely accepted and never questioned. I wonder whether the writers really believed in what they were saying or were cynically taking advantage of the dominance of innumeracy.
I think the lack of understanding is genuine. There are some subtle examples as well. For example, the postal service in the UK (Royal Mail) had a target to deliver 95% of letters posted before noon on the following day. A consumer organisation decided to test this by posting a random selection of letters from and to places all over the country and found that something like 50% arrived the next day. The Royal Mail was questioned and they made the point that their target was 95% of the real sample - a target that they were in fact meeting. The real sample was dominated was letters to and from major population centres. It's barely possible for a letter from Cornwall to the Isle of Skye, say, to take a single day. But, it can be done between most major cities.

The interview was carried out by a highly intelligent, well respected journalist, who really struggled with this concept. To be honest, my opinion of him went down after that. Not least, because he ought to have been able to work that one out for himself.

It's interesting that type of numeric-logical reasoning is unnatural to many intelligent people.

There was an almost identical episode (pre-Internet) with a national call centre that advised travellers on the cheapest option for rail fares. Again the target was to give the best advice in 95% of cases, or so. And, again, a consumer organisation rang them up with a range of the most obscure and difficult cases and found they were unable to get it right 95% of the time.

Hornbein said:
The math of percentages is weird and tricky. If X's salary is double of Y's, then X's is 100% higher.
I never liked the media use of percentages to compare values. You know what it means, and I know what it means, but I seriously doubt that the general reader knows what it means. And as we have seen, some authors don't know what it means. In my view, presenting the comparison as "his 10 million dollar contract is 135 times as much as her 78 thousand..." is easier to grasp.

Klystron
Regarding percentages and their misuse, I've been going to a chiropractor for quite a long time. I've recently been treated for a problem in my shoulder (likely torn rotator cuff). Periodically I'm asked for the percentage improvement as a measure of how well the treatment is going.
My gripe with this, the percentage of improvement, is that it is misleading, and what they should ask me is how I'm feeling in comparison to being 100% cured.

For example, if my self-reported current state is at 30%, a 100% improvement doesn't mean that I am now completely healed, but would get me only to 60%, which is still a long way from my pre-injury state.

phinds
Nowadays simple percentages confuse people. Back in the day Nixon used third derivatives. ("the rate of increase of inflation is decreasing")

Samy_A
martinbn said:
Back in the day Nixon used third derivatives.
And look what happened to him!

Samy_A and hutchphd
And look what happened to him!
Poor Tricky Dicky was a man before his time. If he was President now, he could just have dismissed Watergate as fake news and carried on.

OmCheeto
PeroK said:
Poor Tricky Dicky was a man before his time. If he was President now, he could just have dismissed Watergate as fake news and carried on.
Yeah, what a naive time we lived in back then; even the crooks believed in the rule of law.

phinds said:
Yeah, what a naive time we lived in back then; even the crooks believed in the rule of law.
It may have been more that the US hadn't yet tired of democracy and begun to long for barbarism.

OmCheeto and Hornbein
PeroK said:
begun to long for barbarism.
Hence the 3red derivatives.
At least it hadn't gotten as far as Bessel functions.

(quick PSA reminding folks to stay away from political content in replies...)

gmax137 and PeroK
martinbn said:
[...] Back in the day Nixon used third derivatives.[...]

Probably off-topic but it seems like this thread is kinda degenerating anyway....

Wasn't there something about his wife advising him using astrology or some such bunk?

I'd be surprised that someone believing in astrology would know what a derivative, or indeed just an asymptote, even meant.

That was Regan's wife Nancy

phinds said:
That was Regan's wife Nancy
Yeah but I'd be surprised if something, at least just a little, didn't spill over.
Duh, YEAH. Sorry.

I didn't learn them all in school is my excuse.

phinds said:
TL;DR Summary: CNN makes a blatant math error
Caitlin Clark is set to make $78,000 salary as the WNBA's number 1 overall pick, which is about 137% less than the NBA's number 1 overall pick who will earn$10.5M.

Now, I get that her salary is about 93% of his (which I think is fair to interpret as 93% lower than his), not 137%, but I'm curious how anyone could even GET 137%. I mean, math innumeracy is common but how do you get such a ridiculous answer?

Ibix said:
78000/10.5m ≈ 0.7%, isn't it? So 99.3% lower?

phinds said:
I slipped a decimal point. You are correct. See, I'm allowed math innumeracy also
It's more than just a mistake with a decimal point. $78,000 is not 93% of$10,500,000, nor is it 9.3% of that latter salary. Ibix's point is that $78,000 is about 0.7% of$10,500,000.
phinds said:
That was Regan's wife Nancy
Regan was King Lear's middle daughter. The person whose wife was named Nancy was Ronald Reagan.

Mark44 said:
Regan was King Lear's middle daughter. The person whose wife was named Nancy was Ronald Reagan.
OOPS

phinds said:
That was Regan's wife Nancy
Regan's wife was Ann. Reagan's wife was Nancy.

jbriggs444 said:
Regan's wife was Ann. Reagan's wife was Nancy.
OOPS

Mark44 said:
Regan was King Lear's middle daughter. The person whose wife was named Nancy was Ronald Reagan.
This is making my head spin.

Oops...again, wrong Regan.

phinds said:
how anyone could even GET 137%.
Modern journalism - never let facts get ih the way of a good story. I'm serious. I don't think anyone thought it was important to get the numbers right.

At the risk of discussing content, the four-year contract for the NBA's #1 draft choice is approximately the same as the total annual WNBA ticket sales across all teams.

phinds
I ran into an interesting subreddit recently - r/confidentlyIncorrect
Simple math blunders are quite popular there, after reading dozens of them a pattern emerged.

Usually it's in the form of if you have 600 million dollars and there are 300 million americans, you can give every american 2 million dollars - notice what's going on here - treat the numbers and the descriptors as seperate things - so 600/300 = 2, and append "million".

The other popular post on there is "solve <simple problem statement>, DONT USE CALCULATOR", that usually involves order of operations and never has any parentheses. [Example]

Some people never acquire the correct mental models to deal with even simple math. As a programmer - they tokenize the sentences all wrong. For most people "600 million" is one token that gets converted into the mental representation of a large number. For others "600" and "million" is seperate.

I have like a tier list of common mathematical confusion:
1. 600-million class, like above.
2. Order of operations class.
3. Percentages - they are quite tricky.
4. Probability - human brains not built to handle this well (or probably just not educated)

For myself, I find that 1 and 2 are automatic, 3 sometimes automatic, sometimes I have to stop and think whether a situation falls into the weird edge case, 4 - stop and carefully think through the situation 90% of the time.

While baffled by ubiquitous use of percentages in media publications when simple arithmetic would suffice, my pet peeve concerns units of measurement. One supposes journalists wish to provide reference objects common to their readers, but a beached whale, for example, has length "some percentage of a football field" and masses "how many jumbo jets?".

At least once a year I ask my daily (American) 'newspapers-of-record' to at least use SI units, if only parenthetically. "One meter is approximately one giant step; close to one yard."

PeroK said:
What they meant was that his salary is approx 137 times larger than hers. 137 being, of course, the fine structure constant!
Isn't 137 approximatey 1,876,900% of the fine structure constant's actual value?

Mark44 and Bystander
kuruman said:
Isn't 137 approximatey 1,876,900% of the fine structure constant's actual value?
Possibly, but if so, I am sure it is fully explained in The Hitchhiker's Guide to the Galaxy"

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