Misleading using numbers

Advertising has ALWAYS had an agenda to sell you something and, quoting the experts from Gruen Transfer, it’s about getting you to “feel something” or to “imagine something” or to surreptitiously get you to “lead yourself into believing something that is not actually claimed in the advertisement”.
And if you have led yourself into believing something that is not actually claimed in the advertisement, then you only have yourself to blame when you find it’s not really true. You cannot say the advertiser has misled you!

And of course leading you into believing you are getting something for nothing eg BOGOF sales. (buy on get one free).

The Telstra TV commercial about their smart WiFi modem is an example of getting you to imagine something. The WiFi signal is depicted as snaking it’s way throughout your house, seeking out your devices, leading the ignorant into believing all sorts of bollocks. The truth is that WiFi travels in straight lines, it does not snake it’s way through doorways and hallways, and it does NOT home in on your devices.

It pays to be cynical, being mindful that the goal of advertising is to sell you something, not present you with a balanced bunch of truth and facts.



Do you have any examples where this is done using numbers?

Report calls out ‘mistruths’ on $40b spend on Indigenous Australians

Wow 40B dollars! That is huge! Are all those indigenes rolling in it?

Yet they live much shorter lives with much poorer heath. Their education is seriously lacking and they are incarcerated far more often. By almost any measure of society’s welfare as a group they tend to be worse off.

So is spending that much a sign of wasting public money or just a made-up number with very little significance? If the former does that mean the recipients are already getting plenty from the public purse? Why would such a number be spread about?

You cannot know anything about what a big number means unless you study its origin and context. Big numbers are not intrinsically important, they must have context, but some who generate them don’t want you to think that way.


Its that ham time of year and the question of the safety of eating processed meats comes up.

On the topic of the health consequences of consuming processed meats containing nitrates or nitrites a well known consumer journal told us:

According to the IARC, the more processed meat you eat, the higher the risk – it found that every 50g portion of processed meat eaten daily increases the risk of colorectal cancer by 18% over the course of a lifetime.

“On average, people’s risk of developing bowel cancer by the age of 85 is about 8.2 per cent, so it’s increasing that level of relative risk,” says Hughes.

So for the purpose of understanding what these two paragraphs mean let us assume that our patient whose name is X is newborn into a family that does in fact consume 50g of processed meat per head per day. I ask that we assume that this is a statistically representative family and that they have typical base risks and that they eat representative processed meats in the specified amount. The new parents are pondering on behalf of X the decision whether to eat less bacon and ham or not to worry.

To start with and make things simple let us also say that 85 is a lifetime or close enough and that colorectal and bowel cancer are the same thing. The question that needs answering is; given the two statements quoted above what is X’s approximate risk of developing bowel cancer in their life if they eat as the rest of the family does?

  • about 8.2%
  • about 26.2%
  • about 9.7%
  • another number not listed
  • impossible to say even approximately on the data available
  • I am really confused
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Please, let us not get into how much bacon you eat or whether you like the research on the topic but stick to the logic and mathematics of the two statements. I want to know what they mean to you.


There is a risk of colorectal cancer regardless of eating processed meat or not. The 8.2% average includes all levels of consumption in the calculations, it is based on how many people get the disease and some will eat processed meat every day, some occasionally, and some not at all. Risk for that particular family will involve a number of factors including if they have a genetic disposition to the disease and other factors that increase or decrease the risk. So all that could be said is that the consumption every day would very likely increase the risk as nitrates and nitrites are known risk factors. However that total risk may be greater than, less than, or equal to the average risk.


Each real family and individual have their own characteristics. In this case ‘a family’ is just a manner of speaking, they aren’t real. I framed it around a family to make the question more concrete and relatable to the reasons why we read articles about the subject of identifying healthy eating. I could have put it in terms of abstractions about the whole population where the individual characteristics disappear but that leads into much more complex statistics and epidemiology which would distract from the question of what the two quoted statements mean together.

I ask that we assume that this is a statistically representative family and that they have typical base risks and that they eat representative processed meats in the specified amount.

If that is OK can you then say anything about how much change there is likely to be in the chance of X getting bowel cancer during their life depending on whether they follow the family tradition of eating processed meat?


These sorts of statistics (which are often quoted) are highly misleading. How much of the increase in cyclist deaths is due to increased exposure ie a lot more people riding a bike. As another example, since I ride a motorbike, I’ve tracked road toll stats in Victoria for many years. For quite a few years the incidence of m/c deaths seemed to be increasing, leading to all sorts of calls from the usual suspects for more regulation of motorbikes. But when you look at the death rate per 100,000 bike registrations, the rate actually fell.


A good example, increased casualties does not necessarily mean increased risk.

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Statistics are the work of the devil since they can be used to prove almost anything.

If one prizes every life lost there is one answer.

If it becomes a statistic argument based on a population increase there is another answer.

Neither is the one and only viewpoint.

No, Some people misuse them to attempt to prove almost anything, both through ignorance and intent.

The old saw about lies, damn lies and statistics is a comment about the ability of untrained people to use and understand statistics not the underlying reliability of the mathematics applied to the world.

True, people are entitled to a view. However, whether there is an epidemic or a crime wave or not, or if certain vehicles are more dangerous than others, or if the risks on the road are altering, are all questions that have definite answers - subject to availability of data - rather than opinion.

If you phrase your questions carefully you have a better chance of avoiding silly arguments and getting answers that are useful. Another side of the same problem is stating conclusions in language that is meaningful and supported by the stats.

One change by the Vic Transport Accident Commission to note:

Perhaps closer to what has been the accepted messaging for accidents and injuries in the workplace. However the statistics are presented the targets are the same. Zero lives lost, Zero harm, zero injuries, …

No further comment - noting there is no one perfect measure. A choice of 3 to choose between.

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From Auntie ABC.

The debut of NASA’s X-59 quiet supersonic aircraft is hoped to revolutionise commercial air travel in the US, paving the way for flights that can travel faster than the speed of sound.

The aircraft, which is expected to travel at 1488.64 kilometres per hour, was unveiled at a facility in Palmdale, California.

Can anyone see a problem here?

Apart from being considerably slower than Concorde flew, no.

Not that I can see.

From the ‘salesmen’s mouth’. (always trustworthy, never any over-confidence, etc etc :expressionless: ) As an aside, the Lockheed web site has to be the most unfriendly I have yet encountered regarding cookie management. Perhaps the US DoD wants a list of everyone who has visited?

Supersonic speeds are banned over populated land masses because of the sonic booms (noise and potential damage). If their sonic boom can be eliminated or made ‘safe and acceptable’ that ban could be lifted at the stroke of a pen. As far as Air Traffic Control, supersonic aircraft (Concorde era) were cleared to cruise at altitudes above all other categories of aircraft save for certain military flights.

Considering climb, acceleration, and descent profiles a commercial aircraft built to ‘this formula’ probably would not be as impressive as the potential speed suggests for domestic/continental service.

The question was directly related to the topic.

The linked article says:

The aircraft, which is expected to travel at 1488.64 kilometres per hour

NASA says:

Its design research speed will be Mach 1.4, or 925 mph, flying at 55,000 feet.

The number in the article is misleading and could easily confuse the naïve reader. One obvious question would be “how do they get it to fly at that exact speed and why would they bother?”.

A speed of Mach 1.4 at the listed altitude is in fact close to 925 mph, but the estimate is only to two significant figures, so its design speed is somewhere between Mach 1.3 and 1.5, converting to 925 mph is already stretching the precision. The speed of 925 mph converts to 1488.64 kilometres per hour. Using that number is not warranted nor as informative as it could be.

At the specified altitude Mach 0.1 is about 100 km/h, so converting to 1488.64 is torturing the number into a shape that was never imagined as NASA inferred 1500 ± 100.

A much less misleading statement would be:

The aircraft, which is expected to travel at approximately 1500 kilometres per hour

Which is two significant figures, not six. You cannot create another 4 digits of precision out of thin air.

For the general purpose of the article this probably doesn’t matter very much but it was in the news so I used it as an illustration of false precision. If you are going to quote numbers knowing and conveying their precision is important.

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Remember the information Aunty published comes from the USA, a bastion of their own ‘metrics’ ( :laughing: )

925 mph is fed into a converter for international consumption and voila, the media publishes it. How many journalists have studied or worry about significant digits when there is a story to be told and a deadline to publish it?

For any given medium, and for air as the obvious, the speed of sound varies at altitude and temperature. In a perfectly scientific literate world it reinforces a mach number with some rounding makes sense, but if that was done would pundits be equally put off if they published a rounded approximation that was not the target speed of this experimental aircraft and called it ‘lazy’?

As an example, Concorde could supercruise at mach 2.04 at 60,000 ft. Most flights were between 50~60,000 ft cruise, not all at 60,000ft (+/- allowable IFR margins). It is often called mach 2 in the context of Concorde, not mach 2.04.

Whether that reinforces your contention or not is for an individual to decide if it in fact matters in this instance, or a few extra significant digits matter in the general case.

As I consider your comment it increasingly has scientific and technical validity, but do not agree your example is in any way misleading.

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Ah the age-old problem of numbers. Integer vs real numbers. A source of many problems in data representation in computers.

On one hand, 925 as an integer, is exact. In decimal it would be 925.00000000000000 or however much precision one wants. On the other hand, 925 could be an approximation of a real number truncated or rounded to a value that is an integer.

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How many get told to write stories about technical subjects they have no background in and thereby mangle the facts?

I do not think that everybody must agree with me about the level of inaccuracy of reporting but it does exist and it it could be done better. Finding reporters who have scientific backgrounds sufficient to improve the quality of news may be a practical difficulty but finding those who can use simple numbers correctly ought not be - it isn’t something that takes years of study - mainly it is awareness of the problem. Which is the purpose of this topic.

The issue is that 1488.64 has several digits that have no meaning.

The principle of sticking to the level of precision that the data supports applies to numbers in any format, any base and any computer representation. Inexactness of floating point representation is also a real issue but in another domain.

Should this aspect be equally or more at home in the discussion on ‘e weights’? :wink:

1 kg (e) of mince is accurate enough at some grocers but not others who label and price it as actual weight to the gram in the shops I frequent.

My point is a few extra meaningless digits rarely misleads as I see it, excepting when a utility bill does not add up because of unprinted truncation.