Misconceptions of numbers in everyday life (2 Viewers)

[Trebla]

Numbers and data are everywhere and are an important part of our everyday life. The we way we interpret these numbers impacts our decision making and our opinions of certain aspects of life whether they be in a personal or professional context.

However, many people (including the well educated and intelligent) are susceptible to misinterpreting everyday numbers (sometimes quite often) and there are many examples of this. A major part of this is the lack of understanding of probability and statistics which are incredibly useful tools to make valuable meaning of numbers.

In this thread, I will regularly post examples of common misconceptions of everyday numbers and in the process discuss some fundamental probability/statistics concepts which are often misunderstood, thus leading to this misconception.

Hopefully, this will increase your awareness of commonly held misconceptions of everyday numbers and help you become better informed at interpreting them in your everyday life. Feel free to add some examples to the discussion as well as there are plenty of them out there.

 

[Trebla]

Start off with a simple example for discussion, see if anyone can explain this example of a misconception:

The weatherman's forecast states that "there is a 99% chance of rain tomorrow". It turns out that on that day it didn't rain at all. People will then often say that the weatherman's forecast statement is therefore wrong.

 

[Sy123]

Start off with a simple example for discussion, see if anyone can explain this example of a misconception:

The weatherman's forecast states that "there is a 99% chance of rain tomorrow". It turns out that on that day it didn't rain at all. People will then often say that the weatherman's forecast statement is therefore wrong.

The town may of been lucky enough to get that 1% chance, likewise, if the weatherman made the same forecast for 1000 days and on all days they did not rain, that is not enough to say that the weatherman was wrong.

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In a game of roulette, the ball falls on black the first two rolls, then for the next 10 rolls the gambler bets on red, and each of the following 10 times, the ball landed on black

 

[InteGrand]

Don't know how roulette works, but as long as something has a nonzero probability of occurring, it doesn't mean it can't happen, it may just be unexpected if it happens.

 

[Sy123]

Don't know how roulette works, but as long as something has a nonzero probability of occurring, it doesn't mean it can't happen, it may just be unexpected if it happens.

Yeah, people call it the Gambler's Fallacy http://en.wikipedia.org/wiki/Gambler's_fallacy

People think the probabilities should "balance out", so that after the first 2 blacks, the probability should balance out or something

But really, each roll of the roulette is independent so it is irrelevant what the previous results are

 

[InteGrand]

If I toss a coin a thousand times and get heads each time, can I say anything about P(heads) for that coin (other than that it's not 0)?

 

[seanieg89]

Probability zero things can still occur...

What is the probability of a random number chosen in [0,1] being 0.69? It is 0, yet this can happen.

This is the difference between "surely" and "almost surely".

 

[InteGrand]

Is it said that 0.69 would "almost surely" not be chosen?

 

[seanieg89]

Is it said that 0.69 would "almost surely" not be chosen?

Yes.

 

[Kaido]

Ofc it had to be that number - 0.69. No other number would fit the deal. trollface.jpg

 

[D94]

Start off with a simple example for discussion, see if anyone can explain this example of a misconception:

The weatherman's forecast states that "there is a 99% chance of rain tomorrow". It turns out that on that day it didn't rain at all. People will then often say that the weatherman's forecast statement is therefore wrong.

I'm hopeless at probability but I think in this case, people either think 'it will rain' (100% chance) or 'it won't rain' (0% chance), and they see 99% which is close to 100%, therefore believing it will definitely rain. But when it doesn't, they attempt to rationalise the situation by blaming the weatherman, even though it was their logic that was wrong.

 

[Trebla]

Another one

It is always possible for a person to walk through a river (without being submerged) that is on average 0.5m deep

 

[integral95]

Another one

It is always possible for a person to walk through a river (without being submerged) that is on average 0.5m deep

That statement doesn't mean you are guaranteed to walk through without getting submerged, as "always possible" doesn't mean certain or 100%.

So the opposite is could occur as well.

 

[seanieg89]

That statement doesn't mean you are guaranteed to walk through without getting submerged, as "always possible" doesn't mean certain or 100%.

So the opposite is could occur as well.

I think you are missing the point of this example...

The information given is that the river's average depth is 0.5m, the erroneous conclusion is that a person can cross this river. What is wrong with this deduction?

 

[integral95]

I think you are missing the point of this example...

The information given is that the river's average depth is 0.5m, the erroneous conclusion is that a person can cross this river. What is wrong with this deduction?

oops I missed that.


So you're only given the average depth of the river, however it doesn't give the depth of the deepest region of the river where it could possibly be much greater than your height(like 5m). So it's still possible to drown at the given river since you don't have enough information.

 

[Trebla]

oops I missed that.


So you're only given the average depth of the river, however it doesn't give the depth of the deepest region of the river where it could possibly be much greater than your height(like 5m). So it's still possible to drown at the given river since you don't have enough information.

Yep. Whilst the example is quite obvious, it highlights the very common error of people applying averages to individual members of the population when there is almost always a variation around the average which could be of any magnitude.

Another example of this is in finance where one can easily determine the average return of an investment to be something like 10% which looks good on paper but you also have to consider the variance of the return (also interpreted as the risk of the investment) because it is certainly possible that the investment could be swinging up and down wildly and just happens to average to a nice 10% return. By taking on that investment you are accepting the risk that your investment could potentially swing wildly to something terrible like -50% return in reality.

 

[Trebla]

Here is another one:

A total of 214 people with drugs were arrested at the Field Day music festival in Sydney (setting a record for the New Year's Day event) compared to 140 last year. This means that more people carried drugs in the 2015 festival than the 2014 festival.

 

[Carrotsticks]

Here is another one:

A total of 214 people with drugs were arrested at the Field Day music festival in Sydney (setting a record for the New Year's Day event) compared to 140 last year. This means that more people carried drugs in the 2015 festival than the 2014 festival.

# people getting caught =/= # people carrying drugs.

Consider this scenario:

2014 --> 500 people carrying drugs but only 140 were arrested.

2015 --> 300 people carrying drugs but due to stricter security, 214 people were arrested.

 

[Sy123]

The crime rates of Australia have been decreasing since the introduction of new policing policies, which since the policies have started, the police have gained greater power and abilities. Therefore, the increase in police power has led to the decrease in crime.

 

[Trebla]

There are actually two basic concepts in statistics involved around these statements (or the misuse of them). Anyone know what they are?