Yves here. One of my pet peeves is how people treat arguments that incorporate figures as being more solid than ones that are based on qualitative analysis…even though the data were typically developed using methods that make them far less solid than they seem (see an article I wrote on that issue in 2006).
This post sets forth some of the most commonly-used “lying with figures” tricks and should help you learn to recognize them and not be taken in.
By Larry Schwartz, a Brooklyn-based freelance writer with a focus on health, science and American history. Originally published at Alternet
Americans, as P.T. Barnum once noted, are not all that difficult to fool, and our nation’s somewhat weak math skills don’t help. A Pew Research Center report issued last year, which studied test results of 15-year-olds, ranked the United States 35th in the world in math. Not only has this weakness in understanding numbers created opportunities for mass exploitation by Big Pharma and other industries, it has led to needless and mostly unwarranted fear. While Americans don’t understand math, be assured that corporations do, and they happily use it to mislead and obfuscate in the name of selling their products.
Big Pharma doesn’t only target consumers with its misleading advertising; it also targets your doctor. And why not? Sadly, a medical degree doesn’t necessarily mean your doctor is a numbers whiz. In a report in the journal Psychological Science in the Pubic Interest on doctors’ ability to analyze relevant statistics, they were asked, “If my mammogram is positive, what are the odds that I actually have cancer?” Doctors were given all the information needed to answer that question accurately, and a startling number of them still got it wrong. In fact, only 20 percent of them got it right. (The answer, by the way, is a 10 percent chance.) Of those who got it wrong, 60 percent erred drastically on the side of doom, saying the chances of having cancer were 80 to 90 percent. So if your doctor was in that group, and you got a positive mammogram result, she would have told you that you almost certainly have cancer.
The pharmaceutical business, no surprise, is a big numbers abuser. How many advertisements have we seen touting the wonders of a particular drug? “Lowers risk of heart attack by 50 percent!” Well, yes it does lower the risk by half. Dig a little deeper and you discover that your risk of heart attack has dropped from two in a million all the way down to one in a million. That’s a 50 percent drop! Of course, your original two-in-a-million risk wasn’t all that risky, and side effects from the drug might include a few nasty things, but hey, details.
This is known as reporting test results in relative, rather than absolute, numbers. Big Pharma is well aware that saying your risk drops from two in a million to one in a million isn’t so remarkable. They also know that using phrases like “50 percent less risk” will fool most of the people most of the time. They can defend themselves by pointing out that they aren’t outright lying, after all. An osteoporosis drug once claimed to reduce hip fractures by the same whopping 50 percent. Again, technically true, and it sounds impressive. Unmentioned was that out of all untreated osteoporosis sufferers, only about two percent are at risk for hip fractures. So the drug reduced the risk of hip fractures from two percent of all osteoporosis victims to one percent of all of them, from two in 100 to one in 100. Doesn’t sound all that fabulous when stated in those terms, especially when taking into account the often higher cost of many of these drugs.
The concept of relative and absolute risk is important. Big Pharma loves relative risk and hates absolute risk. Relative sells pills. Absolute, not so much. Any medication can claim to cut your relative risk of getting a disease by huge percentages: 10%, 50%, even 100%. But if your absolute chance of even getting the disease is tiny, than the relative risk, no matter how impressive sounding, is also small. Why take the medicine if you are probably not getting all that much benefit from it? Or why not take the generic lower-cost med that offers more or less the same results?
Cooking the numbers isn’t confined to prescription drug marketing. It wasn’t that long ago Colgate was advertising that 80 percent of dentists recommended its toothpaste. And it sure seemed convincing! Eight out of 10 dentists recommended Colgate, and one was supposed to extrapolate that only 2 out of 10 recommended other brands. That’s a landslide. Better buy Colgate!
Hold on. A closer look at the study which yielded that result showed dentists were asked what brands they would recommend and were allowed to choose as many as they wanted. So yes, eight out of 10 dentists chose Colgate. But eight out of 10 may also have chosen Crest or Aim or any number of other brands. No surprise, the ad was eventually banned as being misleading.
In the late 1990s, Centrum, the vitamin maker, made the alarming claim that nine out of 10 Americans were not getting all the nutrients they needed from what they were eating. Ninety percent of us were deficient! We better buy Centrum to make sure we get the proper nutrition. And that is essentially the message of all vitamin manufacturers.
The numbers, however, have obscured the truth. Centrum got those numbers from a completely unscientific survey taken between 1976 and 1980 in which Americans were asked what they ate on the day of the survey. Only nine percent of the participants said they remembered eating their recommended daily allowance of fruit and vegetables. So nine out of 10, or a whopping 90 percent, did not eat their daily allowance that day. Left unsaid was that any one of the 90 percent “deficient” may have eaten more then their daily allowance the day before, or would eat more the day after. A one-day survey is not an adequate sample to indicate overall diet. Not to mention the fact that adequate nutrition can be obtained from other sources and need not be measured in recommended daily servings. For instance, a 15-minute walk in the sun might get you plenty of vitamin D. But information like that doesn’t sell any vitamins. And so far no one has figured out how to charge for sun rays.
A misunderstanding of numbers can also lead to fear-motivated behavior, and you can be sure the marketers are aware of that fact. In 1995, a warning was sent to almost 200,000 doctors and pharmacists in the U.K. that a new iteration of a popular birth control pill could increase the risk of life-threatening blood clots by 100 percent. That sounds terrifying, right? 100 percent! It was enough to get many women to discontinue using the pill. That action helped contribute to 13,000 abortions the following year. The actual risk? The older generation of the pill had a one in 7,000 risk of blood clot. The new generation had a two in 7,000 risk. A 100 percent increase, yes, but in absolute terms, the risk went up from .014% to .029%.
This past year it was announced that the World Health Organization was classifying bacon as a group I carcinogen. Bacon-lovers despaired. It seems that eating two slices of bacon increases the risk of colorectal cancer by 18%. Misunderstood by the public was that this was the relative risk, not the absolute risk. More plainly, taking in the entire population, the risk of getting colorectal cancer at all is about 5%. So if you eat two slices of bacon, your 18% increase of risk is 18% more than your absolute 5% chance. If you are a typical math-adverse American, your head is spinning right now, but what this means is that your overall risk goes from five in 100 all the way up to six in 100. Not exactly a jaw-dropper when put in those terms.
Politicians and their marketers have learned their business lessons well when it comes to using numbers to strike fear in the populace and sway opinion. Politicians routinely spew numbers that, under scrutiny, either don’t add up or are just plain wrong. They know most voters can’t, or won’t bother to add them up or find out the actual truth, and that when people hear numbers, they naively believe they are hearing something scientific, or based in reality. Michelle Bachmann told us in 2013 that “70 cents of every dollar spent on food stamps goes to bureaucrats.” The fact that only one third of one percent goes to bureaucrats shouldn’t stand in the way of a good statistic. Rand Paul told us last year that, “nine out of 10 businesses fail,” as he sought to blame President Obama for wasting tax money on businesses like Solyndra, the solar panel maker. The actual failure rate is about 50 percent after five years.
And then there is the Donald, whose supporters tend to believe because he is a successful, and as he says, “very rich” businessman. In trying to appeal to his conservative base, Trump ran off a series of murder statistics in a tweet this year that was striking in its claims. Only 16 percent of Caucasians were killed by other Caucasians. (Wrong. 82 percent is the correct figure.) Ninety-seven percent of African Americans were killed by other African Americans. (Wrong. 90 percent is the correct figure.) Eighty-one percent of Caucasians were killed by African Americans. (Wrong. Only 15 percent.) Just two percent of African Americans were killed by Caucasians. (Wrong. 8 percent.) Trump used his false statistics to cast black people as the culprits in white murders when the truth is white people are mostly killed by other white people. And even more true is that most murders happen among people of the same race.
In another statement, Trump called for the cessation of all Muslim immigration, based on a survey he cited which said that 25 percent of those polled agreed that “violence against Americans here in the United States was justified as part of the global jihad,” and that 51 percent agreed that “Muslims in America should have the choice of being governed according to Shariah.” Utter hogwash. That “poll” was conducted by a virulently anti-Muslim organization, the Center for Security Policy. Beyond that, the poll itself was fatally flawed, being only an opt-in online survey with a small sample size of only 600, using a question format (agree/disagree questions) that statistically people have been shown to answer “agree” to, and targeting a population (U.S. Muslims) many of whom are first-generation with limited English proficiency. Moreover, the survey participants were U.S. Muslims, meaning their answers, accurate or not, had no bearing on the Muslims Trump was proposing to bar.
If it sounds like we’re picking on Republicans, it’s because there is cause. A study from the non-partisan Center for Media Studies in 2013 came to the conclusion that Republicans lie three times more than Democrats. And a favorite method of political lying is the misstatement of numbers. Politicians and industry and charlatans get away with it because numbers sound impressive to people who don’t understand them, and this includes the mainstream media that reports the numbers without challenge, as if they were fact. If we hear fancy sounding numbers and math intimidates us, we tend to accept the truth of what we are hearing because math has street cred. Mathematicians are smart, and if someone strings together a bunch of numbers and looks confident, we will, more often than not, accept their “smartness.” To paraphrase a famous wizard, “Pay no attention to those numbers behind the curtain!” And so we don’t, especially if the alternative is to do our homework and better understand the math.
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I hypothesize that the structure of the imperial system of weights and measures is responsible for some of the aversion to math in the US. IMO there are too many structures to remember for school age children who are also learning other subjects at the same time. Of course many people quite simply dislike or are not suited to working with numbers, regardless of the system used. I expect that frustration in the early stages leads to a life long aversion to math for many. I expect common core math also contributes to this, from the little of it I have seen.
It seems there is at least one frequent commenter here who is very attached to the imperial system, to the point of declaring that the metric system was implemented due to lack of penis size, so I have donned my flame proof suit and look forward to reading any rebuttals to my comment.
(Btw I have no intention of making this my pet issue and trying to shoehorn it into discussions, however it seems appropriate here.)
Ya, it hard to count to 16 on the firngers of one’s hands, and the toes are too far away to be useful, except in the frequent cases of putting one’s foot in one’ mouth.
And it is so easy to divide a dollar, 100 cents, into 3 equal parts.
And it is so easy to divide a dollar, 100 cents, into 3 equal parts.
Ha. That’s why all prices end with 99 cents.
That’s selling psychology, not the number base system. $4.99 vs $5.00.
I’m not trying to sell psychology to anyone!
You misunderstand. ‘”selling” psychology, as in ‘what it takes to get people to buy’; not as in, ‘pushing psychology as a thing in itself’. See: Edward Bernays. Perhaps I should have used quote marks.
Nice to see some joking around. Bernays position in our world is astonishing. I have to say that he had little need of numbers. He was about imagery. I am thinking of the Easter Parade and photographs widely circulated of fashionable and sophisticated women smoking that worked so well for the tobacco industry.
His work as was, was it Public Relations? Minister of Propaganda might have been the greater truth. He worked for Woodrow Wilson and in 6 months with his posters isolationism was turned to the Grand mission to fight the war to end all wars, right all wrongs, make the world safe for Democracy. Young men climbed over each other to go to the trenches. My people had R. Crumb, and the Fillmore. Woodstock became Woodstock Nations. Whatever the dreams of Woodstock Nation were, they sold jeans and head scarves in the end. All wiped away, co-opted with a last gasp of Peter Max posters. Marshall McLuan killed it making it all the more meaningless.
Yeah they do a good job of selling lies, when they put them in the mouths of some doctor, or a guy in the right pants. But I still think it is the picture, replays of just the wrong laugh, or a scream, remembering that poet ran got pictured looking silly in a tank.
This was a very important essay. I cannot praise Yves Smith enough. I’ve been posterized by a guy over in Germany. I hope he sells lots of them.
Thank you Larry Schwartz
It’s my belief that low_integer is being surreptitiously funny.
And a low integer is the point of the low mathematical IQ of Americans. (1000 x zero is still zero.)
Oddly enough, the $4.99 price (or $0.99, etc.) was not devised by marketers. It was a natural process developed by small business owners who wanted to make sure the clerks ran up sales on the register rather than pocketing the cash themselves. Selling a $5 item for $5 means a five dollar bill and the temptation to steal. If it’s $4.99, the clerk has to make change. When he rings the sale, the register goes “ding” and the owner can hear it from the back room or wherever.
Yep. Is that the reason we Canadians have rejoiced that the Canadian dollar is now worth .69 cents against the Mighty ;anti-metric U.S.A. dollar?
Milk with 2% fat is so much more healthy for me than whole milk. Nope, it’s not a 98% reduction in my intake of milk fat it’s really 33%.
This brings to mind the Reinhart-Rogoff study identifying 90% as the jumping the shark point in a country’s debt/GDP ratio on the path to the economic damnation. That study gave the money lenders quantitative ammo in their selling of austerity and the turning of Europe into a fire sale for private investors. Turns out the study was flawed. One problem being an Excel coding error. The study continued to be widely cited anyway. Then you have politicians like Trump who literally pull black on white crime figures out of the air to sell racial fear. The percentage sign behind a number today is as sacrosanct as St in front of a name was in medieval times.
Even if we allow the Excel error, and lumping things together that might not go together, the 90% number is hardly a threshold. All you have to do is look at the graph to see that. It is an artifact of the grouping of data in the study. Surely R&R had the mathematical sophistication not to make that error in interpretation. Yet they not only did so, they sold the idea to a group of Senators in the winter of ’09 and ’10! Before publication.
“There is no means of human communication which may not also be a means of deliberate propaganda, . . .”
Edward Bernays in ‘Propaganda’.
“There is no use to talk to much, for men who do so may tell lies.”
A Wichita (American Indian) Chief
“Men in general are quick to believe that which they wish to be true.”
Julius Caesar
I believe that last quote is Shakespere, not JuliusCeasar himself.
See https://en.wikiquote.org/wiki/Julius_Caesar, “Fere libenter homines id quod volunt credunt,” which can be translated various ways but gets at the gist.
Yeah, that mass-murderer sure could write.
Great article! Nice to put the numbers on the numbers.
Over time, I have come to assume anything said on TV that couldn’t be verified by looking out the window was more likely to be false than true but I WAS lazy and didn’t do the math. Well, it turns out they hit the 100% mark in 1990 and have been lying more and more frequently ever since!
. . . A study from the non-partisan Center for Media Studies in 2013 came to the conclusion that Republicans lie three times more than Democrats.
My study has found that 98% of politicians are narcissists, and they lie for a living, irregardless of party affiliation.
From the linked study.
On this surface the fact that Republicans lie more than Democrats may appear obvious, but beyond the numbers this study confirms that lying is a major component of Republican political strategy.
Lying is a major component of any politician’s strategy and to claim Democrats lie at a rate one third of Republicans is itself a lie.
” Norman, listen carefully……..Everything Harry tells you is a LIE”
It’s a shame that the average “educated” American still has a sub 80 IQ when it comes to political or economic policy assertions by any politician, whether R or D. Anyone with access to an objective evaluation of events and who can connect dots can spot the lies, obfuscations and disinformation. The amount of hypocrisy and condescension towards the American people is endemic to all politicians and policy makers, regardless of affiliation.
I spend an embarrassingly large amount of time following professional ice hockey, and there is a fairly large contingent of fans who do their own analysis for their favorite team on a level that almost certainly rivals that of the franchises themselves. They give nuanced views about things like salary cap implications for free agent contracts, the worth of draft picks relative to other organizational assets, and estimate player value by churning enormous amounts of data through spreadsheets. When the discussions on these sites venture into politics, I find that some of these same people are the idiots I see posting under MSM articles whom I assumed incapable of anything resembling critical thought, and I’m reminded of a Chomsky quote:
Well, let me give an example. When I’m driving, I sometimes turn on the radio and I find very often that what I’m listening to is a discussion of sports. These are telephone conversations. People call in and have long and intricate discussions, and it’s plain that quite a high degree of thought and analysis is going into that. People know a tremendous amount. They know all sorts of complicated details and enter into far-reaching discussion about whether the coach made the right decision yesterday and so on. These are ordinary people, not professionals, who are applying their intelligence and analytic skills in these areas and accumulating quite a lot of knowledge and, for all I know, understanding. On the other hand, when I hear people talk about, say, international affairs or domestic problems, it’s at a level of superficiality that’s beyond belief.
In part, this reaction may be due to my own areas of interest, but I think it’s quite accurate, basically. And I think that this concentration on such topics as sports makes a certain degree of sense. The way the system is set up, there is virtually nothing people can do anyway, without a degree of organization that’s far beyond anything that exists now, to influence the real world. They might as well live in a fantasy world, and that’s in fact what they do. I’m sure they are using their common sense and intellectual skills, but in an area which has no meaning and probably thrives because it has no meaning, as a displacement from the serious problems which one cannot influence and affect because the power happens to lie elsewhere.
Well, there’s also the angle that in sports, there’s nothing hidden. All the data people need is laid out in detail. This isn’t true of politics. All data there is liable to be false, gamed, or simply entirely missing unless you have the guts to dig around on ‘conspiracy’ sites and then work out whether what you find is accurate or not. This takes an enormous amount of sheer labor.
There are 3 kinds of people in the world: those who can count, and those who can’t.
Don’t forget the obverse side of the coin–when it comes to policy discussions involving large numbers, the corporate media deliberately use “huge” absolute budget numbers (confusing, scary!) rather than relative versions (0.05% of an overall amount.) The latter would contextualize things so that rational decisions can be made. Dean Baker is of course the main point person calling on the mainstream media to present the context, with relatively little success so far.
Another related issue is that the budget numbers are always expressed in ten-year totals. Why? Why don’t we talk about the effect of policy on the next year’s budget, not the next ten years? I think this has been promoted by neo-liberal think tanks such as the Peterson Institute simply to make us talk about bigger, and therefore, scarier numbers. It sounds far worse that a government program will cost $125 billion over ten years than to say it will cost $12.5 billion next year. It’s the big number that sticks in people’s minds, not the time period.
IIRC, the Peterson Institute wants the government to start using 75-year projections in reporting budget numbers. (I know this sounds crazy, but hey, it’s the Peterson Institute).
And, Paul is correct, using percentages would promote far more rational discussion. For example, on average, people think that 28% of the federal budget goes to foreign aid. The actual amount is about 1%.
So if a Democrat tells the truth about the cause of 3 problems and then lies that he will do anything to fix them, that only counts as 1 lie.
But if a Republican lies about the cause of 3 problems and then tells the truth about his plans to “fix” them, that counts as 3 lies.
If . . . then. . . ; if. . . then. .. .
If a Republican lies about the cause of six problems and then lies about his plans to fix them he tells six lies and he is a liar. If a Democrat tells one lie then he is also a liar.
something like that,.. yeah
My pet peeve, and often found here at NC: “gun violence,” which when you read the fine print is actually mostly suicides which would happen even if there were no guns (see Japan and Korea). This is a deliberate spin to make it look like we have a big gun problem when actually the murder rate has been declining for decades.
If suicide by gun is “gun violence,” then shouldn’t suicide by hanging be “rope violence?” Overdose should be “pill violence,” drowning should be “water violence,” car accidents should be “vehicle violence,” etc. ?
Another pet peeve: “the mentally ill are more likely to be victims of violence than perpetrators of violence.” Ummm, NRA members are more likely to be victims of violence than perpetrators of violence. WE’RE ALL MORE LIKELY TO BE VICTIMS OF VIOLENCE THAN PERPETRATORS OF VIOLENCE. That’s because most of us are non-violent and a small percentage of the population commit most of the violent crimes. But the fact remains that SOMEONE commits those acts of violence and a disproportionate percentage of people convicted of violent crime are mentally ill.
The gold standard for measuring the level of violence in a society is the murder rate. Most crime goes unreported, but we do a pretty good job of keeping records of dead people.
Another one: the unemployment rate. We don’t actually measure how many people are unemployed and we can’t even agree on what it means to be unemployed. On the other hand, we do know how many people are employed because those people have to pay payroll taxes (unless they work off the books). So the gold standard for measuring employment should be the employment rate — workforce population or the employment/population ratio — not the unemployment rate.
– “Although studies suggest a link between mental illnesses and violence, the contribution of people with mental illnesses to overall rates of violence is small, and further, the magnitude of the relationship is greatly exaggerated in the minds of the general population (Institute of Medicine, 2006).”
– “…the vast majority of people who are violent do not suffer from mental illnesses (American Psychiatric Association, 1994).”
– “The absolute risk of violence among the mentally ill as a group is very small. . . only a small proportion of the violence in our society can be attributed to persons who are mentally ill (Mulvey, 1994).”
http://depts.washington.edu/mhreport/facts_violence.php
“suicides which would happen even if there were no guns”
Not true. Research has shown that limiting access to the most lethal or most popular means of suicide limits the death toll as suicidal individuals are left to choose from less-lethal or less-appealing means. The choice of means will vary between cultures. In the United States, suicide by firearm is among the more popular methods and by far the most lethal, with a case fatality rate of over 90% compared to 5% for the most common methods of attempted suicide – overdoses and lacerations. In rural cultures of East Asia and the Pacific Islands, pesticides are a leading choice, and restricting their availability has saved lives. The extreme lethality of firearms is significant because over 90% of those who survive a first suicide attempt do not go on to die from suicide.
http://www.hsph.harvard.edu/means-matter/
http://www.hsph.harvard.edu/hicrc/firearms-research/gun-ownership-and-use/
http://www.hsph.harvard.edu/magazine-features/guns-and-suicide-the-hidden-toll/
This article speaks to me. Right now in Canada, the Liberal government is saying that it will create a $10 billion deficit each of the next four years in order to stimulate the economy. Now it appears that with the lower Canadian dollar and the lower oil price, this deficit will probably be much higher. The journalists and opposition politicians are tying their panties in a knot decrying these huge deficit figures! There is a lot of throwing around GDP figures and bewailing the huge debt that will be left to our grandchildren!
We know that once the economy supplies adequate jobs, everyone will be happy and the deficit will have achieved its goal successfully.
Great post. Very enjoyable read. Thanks.
Enjoyed the 2006 article linked in your intro. Unfortunately, replacing experienced judgement with computer model algorithm results continues apace in both business and medicine. The results are less than optimal. This puts the lie to the more grandiose claims made for A.I.
Computers do not make mistakes. Computers just repeat your mistakes endlessly.
They do, in fact, make mistakes. For one, rounding error is a fact that many programmers have to contemplate. I imagine it is also possible for the hardware to err, but I don’t know much about that. (For an example of a calculator error, try asking a Ti-84 to execute (1+1/(10^13))^(10^13). It is an interesting error, which you can research. (I have before, but I ain’t gonna bother right now.) … As I recall, it has everything to do with the choices made by the programmers which resulted in a less than optimal algorithm for this particular function, in regards to rounding accuracy.)
I should have provided I little bit more context. The expression (1+1/n)^n is an approximation for the irrational number e for high n. … Through lots of behind the scenes fiddling, it is possible to verify that the Ti-84’s number is wrong. … Just thought I’d give more context in case you want to research it.
Strange, then, that whenever I challenge errors in billing or other bureaucratic faults the computer is cited as the cause of the error. And just recently the U.S.A. told the Iranians and the rest of the world that a GPS fault led to Goldman Sachs creating faulty mortgages . . . no, no, I’m wrong.
I’m sorry but I get so confused trying to divide everything by the magic 3.
I attribute my problems in numeracy to teachers telling me that one couldn’t subtract any larger number from a smaller number AND then being told, after 8 years, that you could so subtract a larger number from a smaller number and that deficits didn’t matter.
This reminds me of when I studied economics in college. There was “math” in that was were supposed to learn equations, but the equations weren’t really meant to be solved or used for anything. I also always immediately intuited that the assumptions behind said equations were bizarre and nonsensical. When discussing it with fellow students however, they were clueless, and the professor was offended when I mentioned such things.
I now believe that numbers, much like progress and science, have strong religious overtones in our society. Injecting numbers into anything makes it holy and abstruse. It’s incomprehensible, but that’s ok; it should be trusted anyway. Because numbers. I’m frankly exacerbated about how easily people are manipulated, pick up false beliefs, and walk around with faulty and unscrutinized mental models.
I dumped economics when the professor happily differentiated across discontinuities to be able to derive the marginal utility of some investment in new production plant /-p.
It didn’t faze him one bit that – this can be easily shown graphically with a ruler – one could get any slope whatever by moving the points on either side of the discontinuous point in the function, it’s “… just pick two suitable points ….”.
As an Engineer, …well … it’s just not done.
There is no way to learn mathematics by rote memory. One must learn to understand it,
and for that I recommend a good course in geometry. Math can become fun when you
play with it.
Perhaps.
I’d rephrase what you wrote to “Once math is understood, math can be fun when you play with it.”
Pretty much like anything else. Reading and writing and speaking can be fun once you can play but are torture for the illiterate and tongue-tied.
The weather reporters are very good at miss reporting what is a normal daily temperature, they imply any temperature more that a couple of degrees from the average is abnormal, when in reality a range of plus or minus 13-15 degrees is perfectly normal and should be expected.
I once got a dirty look from a meteorology professor when I asked the basis behind the ‘percent chance’ in weather reports. If the report says 20% chance of rain, would that mean that in the roughly 100 square miles of affected area 20 of them will almost certainly get wet but they don’t know which ones?
He never answered the question.