This is How Easy It Is to Lie With Statistics

Summary

This video explores the power and potential misuse of statistics in various scenarios, from marketing strategies like Target's pregnancy prediction algorithm to courtroom cases like the Sally Clark trial. It highlights how statistics can be manipulated or misrepresented, leading to significant consequences in advertising, legal judgments, and public perception.

Takeaways

• 🤰 Target's data analysis identified pregnant customers by analyzing their shopping patterns, leading to targeted marketing strategies.
• 🔍 Statistician Andrew Pole developed an algorithm to predict customers' pregnancy status and due dates, enhancing Target's marketing effectiveness.
• 🤔 Target's approach to sending coupons for baby products was subtle to avoid alarming customers, blending them with unrelated items.
• 😡 A father's initial anger over receiving baby-related coupons turned to embarrassment when he discovered his daughter was indeed pregnant, highlighting the predictive power of Target's algorithm.
• 👵 In a 1964 case, statistics were used in court to calculate the probability of an innocent couple matching witness descriptions, leading to a guilty verdict.
• 👶 The Sally Clark case demonstrated the misuse of statistics in a criminal trial, where the probability of two infants dying from SIDS was misinterpreted, resulting in a wrongful conviction.
• 📊 Misleading statistics can be created by omitting zero as a baseline in graphs, exaggerating differences and potentially influencing public opinion.
• 📈 The UK's advertising standards authority criticized Colgate's claim that '80% of dentists recommend Colgate' due to the misleading nature of the statement.
• 🤔 The difference between a 100% increase in a small number and a small percentage increase can be misleading, as shown in the high school dropout rate example.
• 🔗 Correlation does not necessarily imply causation, as seen in the examples of head lice and health, or ice cream sales and heat strokes.
• 📚 The Simpson's paradox illustrates how data can be misleading when not properly grouped, as seen in the Berkeley graduate school acceptance rates.

Q & A

What was the main challenge that Target presented to statistician Andrew Pole in 2002?

The challenge was to develop an algorithm using only computers to determine which customers were pregnant, even if they didn't want Target to know, by analyzing their shopping patterns.

What common shopping behaviors did Andrew Pole identify among expectant mothers?

Andrew Pole noticed behaviors such as an increase in lotion purchases, loading up on vitamins, and buying other pregnancy-related items, which he used to determine the likelihood of customers being pregnant.

How did Target use the information from the algorithm to benefit their marketing strategy?

Target used the information to send coupons to customers at the right time, corresponding to their pregnancy stages and due dates, even after the baby was born, to enhance their marketing effectiveness.

Why did Target mix pregnancy-related coupons with unrelated products?

Target mixed these coupons to avoid alarming customers who might not have disclosed their pregnancy, making the coupons seem more natural and less intrusive.

What incident led to the revelation of Target's pregnancy prediction algorithm?

A man from Minnesota was upset because Target was sending his high school daughter coupons for baby-related items. Later, he realized that the algorithm had correctly predicted his daughter's pregnancy before he knew about it.

Can you explain the famous case of Janet Collins and her husband Malcolm involving the use of statistics in the courtroom?

Janet Collins and Malcolm were accused of a crime based on witness descriptions. A mathematician calculated the probability of an innocent couple matching all the descriptions, concluding it was less than 1 in 12 million, which influenced the jury to find them guilty.

What is the issue with the claim '80% of dentists recommend Colgate' as used in a 2007 UK advertisement?

The issue is that the study allowed dentists to recommend more than one toothpaste brand, so while 80% recommended Colgate, it was also true that 100% recommended other brands like Crest, which could mislead consumers.

How can a 100% increase sometimes be misleading when describing changes in percentages?

A 100% increase can be misleading if the initial percentage is very small, as it might represent only a tiny absolute change. For example, going from 0.0001% to 0.0002% is a 100% increase but represents a very small actual change.

What is the difference between correlation and causation in statistics?

Correlation indicates a statistical relationship between two variables, while causation implies that one variable causes the other. Just because two things are correlated does not mean one causes the other; they could be caused by a third factor or simply occur together by chance.

Can you provide an example of the misuse of statistics in a legal case?

The case of Sally Clark is an example where the misuse of statistics led to her wrongful conviction for the murder of her two children. The court used the probability of two SIDS deaths in the same family without considering genetic or environmental factors, which later led to her conviction being overturned.

What is the 'Simpson's Paradox' mentioned in the script, and how can it mislead data interpretation?

Simpson's Paradox occurs when a trend appears in different groups of data but disappears or reverses when these groups are combined. It can mislead data interpretation by showing a different overall story than the individual group trends.

What is the 'Prosecutor's Fallacy' and how can it lead to incorrect conclusions in legal cases?

The Prosecutor's Fallacy is the incorrect assumption that the probability of A given B is the same as the probability of B given A. This can lead to incorrect conclusions in legal cases, as it may misrepresent the likelihood of guilt or innocence based on certain characteristics or evidence.

Why are bar graphs that don't start at zero potentially misleading?

Bar graphs that don't start at zero can exaggerate differences between data points, making small changes appear much larger than they actually are. This can be used to mislead viewers by distorting the perception of the data's scale.

Outlines

00:00

🤰 Target's Pregnancy Prediction Algorithm

In 2002, Target sought a way to predict customer pregnancies using shopping patterns. Statistician Andrew Pole developed an algorithm that analyzed behaviors like lotion purchases and vitamin buying to identify expectant mothers and estimate their due dates. Target then sent coupons for baby products at the right time, subtly mixed with unrelated items to avoid suspicion. However, this approach backfired when a man discovered his high school daughter was receiving baby-related coupons, inadvertently revealing her pregnancy before she had told her family.

05:00

🔍 Misleading Statistics in Advertising and Court Cases

This paragraph discusses how statistics can be manipulated to mislead. An example is the UK ad for Colgate that claimed '80% of dentists recommend Colgate', which was misleading because dentists could recommend multiple brands. The paragraph also covers the misuse of statistical probability in court cases, such as the case of Janet Collins and Malcolm, who were convicted based on a mathematician's calculation of their guilt, and Sally Clark, who was wrongly convicted of murdering her children due to misinterpreted statistical evidence.

10:03

📊 The Dangers of Misinterpreting Statistical Data

The paragraph highlights the potential for misinterpretation in statistical data, such as the confusion between percentage increase and absolute increase in dropout rates. It also discusses the misuse of statistics in health scares, like the exaggerated risk of blood clots from a birth control pill, leading to unnecessary fear and consequences. The concept of correlation versus causation is explored, emphasizing the need for careful analysis before drawing conclusions.

15:03

📚 The Prosecutor's Fallacy and Misleading Graphs

This paragraph delves into the prosecutor's fallacy, where the probability of a given event is incorrectly assumed to be the same as the probability of the event given a condition. Examples include a case where an innocent couple was wrongly convicted due to this fallacy. Additionally, the paragraph addresses the misuse of bar graphs that do not start at zero, exaggerating differences and misleading viewers, as seen in various media examples.

Keywords

💡Statistician

A statistician is a professional who deals with the collection, analysis, interpretation, and presentation of data. In the video, the role of a statistician is highlighted through Andrew Pole, who developed an algorithm to predict customer pregnancies based on their shopping patterns, demonstrating the power of statistical analysis in understanding consumer behavior.

💡Algorithm

An algorithm is a set of rules or steps used to solve a problem or perform a computation. The video discusses an algorithm created by a statistician to determine the pregnancy of customers, which is a prime example of how algorithms can be used in data mining and predictive analytics to uncover hidden patterns.

💡Shopping Patterns

Shopping patterns refer to the behaviors and habits of consumers when they purchase goods. The video script mentions how an increase in lotion purchases and vitamins can be indicative of expectant mothers, showing how analyzing such patterns can lead to significant insights in marketing strategies.

💡Data Mining

Data mining is the process of discovering patterns in large data sets. The video illustrates data mining through the development of an algorithm that identifies pregnant customers by analyzing their shopping habits, which is a practical application of this concept in retail marketing.

💡Predictive Analytics

Predictive analytics is the use of data, statistical algorithms, and machine learning techniques to identify the likelihood of future outcomes based on historical data. The video's theme revolves around the use of predictive analytics to send targeted coupons to pregnant customers, highlighting its effectiveness in enhancing marketing strategies.

💡Correlation

Correlation refers to a statistical relationship between two variables. The video discusses the importance of distinguishing between correlation and causation, using examples such as head lice and health, to emphasize that correlation does not imply causation and can lead to incorrect assumptions.

💡Causation

Causation is the relationship between an effect and its cause. The video script warns against the common mistake of assuming causation from correlation alone, as seen in the discussion of violent TV shows and children's behavior, and the tragic case of Sally Clark, where incorrect assumptions led to a miscarriage of justice.

💡Prosecutor's Fallacy

The prosecutor's fallacy is a logical error where the probability of a hypothesis given the evidence is confused with the probability of the evidence given the hypothesis. The video script uses the example of a couple accused of a crime to illustrate how this fallacy can lead to wrongful convictions in the courtroom.

💡Simpson's Paradox

Simpson's paradox is a phenomenon in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. The video script describes a scenario involving graduate school acceptance rates, where the overall data masks the actual acceptance rates when data is grouped by program, leading to a misleading conclusion.

💡Misleading Statistics

Misleading statistics occur when data is presented in a way that creates a false impression. The video provides several examples, such as the representation of tax cut impacts and high school diploma rates, where the use of non-zero baselines in graphs exaggerates the actual changes, demonstrating the importance of careful data presentation.

💡Epidemiology

Epidemiology is the study of the distribution and determinants of health-related conditions in populations. The video touches on this field when discussing the case of SIDS and the statistical evidence presented in court, which is a critical aspect of understanding the prevalence and potential causes of diseases in a population.

Highlights

Target's statistician Andrew Pole developed an algorithm to predict customer pregnancies based on shopping patterns.

The algorithm analyzed behaviors like increased lotion and vitamin purchases to identify expectant mothers.

Target used the algorithm to send timely coupons for pregnancy and baby-related products.

To avoid alarming customers, Target mixed baby-related coupons with unrelated products.

An angry father confronted Target over coupons sent to his pregnant daughter, unaware of her pregnancy.

The father later apologized after realizing the algorithm's accuracy in predicting his daughter's pregnancy.

A mathematician's testimony in a criminal case calculated the probability of an innocent couple matching witness descriptions.

The probability of 1 in 12 million led to a guilty verdict based on statistical evidence.

Sally Clark was convicted of infanticide based on a statistician's testimony regarding the rarity of two SIDS cases.

Misuse of statistics in Clark's case assumed independence of events that were likely influenced by genetic factors.

The misuse of statistics in advertising can lead to misunderstandings, as seen with Colgate's '80% of dentists recommend' claim.

Increases in percentages can be misleading; a 100% increase from 5% to 10% represents a 5% absolute increase.

Headlines can be misleading; a 100% increase in a rare event may not indicate a significant problem.

Misleading statistics on birth control pills led to women discontinuing use, resulting in unwanted pregnancies.

Correlation does not imply causation; head lice were once thought to improve health due to observed correlations.

The third cause fallacy suggests a third factor may be causing two correlated events, not each other.

Simpson's paradox shows that aggregated data can tell a different story than data grouped by categories.

Prosecutor's fallacy arises when the probability of two events given each other is incorrectly assumed to be the same.

Misrepresentation of data in graphs, such as not starting the baseline at zero, can distort perceptions.

Statistics can reveal intimate details of our lives or make trivial events seem serious, highlighting their power and potential misuse.

Transcripts

Back around 2002 target came to a statistician with a question, in which is the answer

could potentially make the company millions of dollars. They asked, "using only computers

can you determine which customers are pregnant even if they don't want us to know?" and

From then on statistician Andrew Pole was in search of an algorithm to do just that

What he did was analyzed the shopping patterns of expectant mothers and noticed some common behaviors like an increase in lotion purchases

Loading up on vitamins and more stuff that I know nothing about and he used this information

To not only determine which customers were likely pregnant

But what their expected due date was and after developing his mathematical model the statistician had a list of hundreds of thousands of women

who were likely pregnant along with their expected due date and what trimester they were in and

From then on target could send coupons at just the right time over the next several months and even after the baby was born

Now, although target was cautious about following secrecy laws. It still might turn women away

if all of a sudden they started getting coupons like cribs and diapers and other related items when they didn't in fact

Tell the company that they were pregnant

So what target did was just sprinkle these items in along with some other unrelated products when coupons arrived so it would seem more natural

But about a year after creating this algorithm something happened though, and this is where it gets interesting

One day a man walked into a Minnesota Target demanding to see a manager

He was very angry

and apparently what had been going on was target was sending coupons for things like diapers and

Cribs and other related items to this guy's high school daughter and he was very upset about this

He was saying things like are you guys trying to encourage her to get pregnant?

And the manager didn't really know what was going on

He of course apologized and a few days later the manager called the dad back to apologize again

But this time the dad wasn't so much angry but a little more embarrassed

I think you guys know where this is going. on the phone The dad said I in fact owe you an apology

There's been some things going on around here that haven't been fully aware of and in fact

My daughter is pregnant and she's due in August

So yes this statistical algorithm figured out that this girl was pregnant before her dad even knew about

That right there is the power of statistics and we're just getting started. In

1964 an elderly woman was walking home from grocery shopping when she was all of a sudden pushed to the ground and had her purse stolen

Now she was able to get a glimpse of the thief and saw a blonde woman in a ponytail who then fled the scene

Then there was also a man nearby who heard the screaming

And saw the woman run into a yellow car that was driven by a black man who had a beard and a mustache

And yes

This is all needed for the story by the way. a few days after the incident police ended up catching

Janet Collins and her husband Malcolm who matched all the descriptions given by the witnesses

They were then charged with the crime and put in front of a jury

now since most of the evidence that could be provided for this was just from the victim and the man who saw the event and

what they both witnessed they brought in a mathematician as well to help prove the guilt of this couple. This mathematician calculated the

Probability of just randomly selecting a couple that was innocent

But also happened to share all these characteristics that were observed by the witnesses. Based on data

The mathematician came up with these numbers and assuming independent events

We can multiply them all together to find the joint probability that they all happened to apply to an innocent couple

Turns out there was less than a 1 in 12 million chance that this random couple who just happen to fit all those descriptions

Was innocent, so the jury returned a guilty verdict

This is actually a very famous case in terms of using statistics in the courtroom. Another quick example

is that of Sally Clark who was found guilty of murdering her two infant son's back in the 90s. Her first son died suddenly in

1996 due to unknown causes so it was assumed it was a case of SIDS, or sudden infant death syndrome

But about a year later she gave birth to her second son

Who was then found dead 8 weeks after his birth again of unknown causes

So after this happened and it was reported, the police ended up arresting her and her husband on suspicion of murder

During the trial a pediatrician professor

Testified that the chance of two infants dying due to SIDS at around the same time relative to their birth

Was about 1 in 73 million and again one in 73 million is way beyond a reasonable doubt

so it was more likely this was an event of shaking or smothering or whatever and

Sally Clark was found guilty and sentenced to life in prison

So you can see statistics has a lot of power in our world whether it be advertising

Criminal cases and so on but what's also really powerful and way easier to do is lie

mislead and misinform

Using statistics and you don't even have to use wrong data to do this

I mean, I've already done that multiple times in this video. I'm going to talk about that soon

so yes this next part for all you people who comment on videos before watching the entire thing because there is more I'm going to

Say but let's start off light though. In

2007 in the UK an ad was released for Colgate that claimed the classic "80% of dentists recommend Colgate"

It wasn't long before the advertising standard authority of the UK ordered they abandon this claim because although it was true

They knew people would not really understand what it meant

The study that was done allowed dentists to answer with more than one toothpaste

So like dentist one might say I recommend Colgate, crest, oral-b

Dentist two might say Colgate, crest, or Sensodyne and similar for dentists three, four, and five

In this scenario 80% of dentists do recommend Colgate. That is true.

But 100% of dentists recommend crest in this hypothetical and 80% recommend oral B as well

All of these numbers are factual and you can make an advertisement with any of these claims

But again, we know people would not understand what they really meant

now for this next part I'm going to ask you guys a question. If

Let's say hypothetically the high school dropout rates of a certain country go from 5% one year to 10%,

Is that a 5% increase or 100% increase?

Because if you're at 5% and you add five you get to 10% obviously

But if you're making let's say $5 an hour and you get a 100% raise you'll be at $10 an hour

So which one of these is it and I'm sure many of you are saying that seems like a pointless question

Yes

You do add five to get to 10, but the physical amount of people who are dropping out would be increasing by 100%

Well in the spirit of this video

Let's ask something else. Which one of these paints a more accurate picture

Like if one of these was posted in the New York Times or on Forbes or whatever

Which one tells the people more about what's going on?

And I'm actually curious what you guys have to say about that because I think we're gonna hear different answers from different people

But for this next part, I think we're all going to agree

What if hypothetically the dropout rates are one in a million people and then the next year they go to two in a million people

So that's .0001% to .0002%, a difference of again .0001

But that's also a 100% increase in the physical amount of people dropping out

So which one of these two headlines do think paints a better picture?

Well again, we might hear different answers

But I think we can agree the 100% makes it seem like a worse problem than it is

Like if five people in the whole nation are dropping out and the next year ten people do I

Wouldn't necessarily call that an epidemic just yet

Now using numbers like this in the misleading way is actually not hypothetical because it happened a few decades ago in the UK

But not with college dropout rates, but rather a birth control pill. In

1995 the UK Committee on safety of medicines issued a warning that a certain type of birth control pill

Increased the risk of life-threatening blood clots by 100%

What that actually meant was that with the older second-generation pill about 1 in 7,000 women developed a blood clot

Whereas with the new pill about 2 in 7,000 women developed a blood clot

So yes, the physical amount of women receiving a blood clot did go up by a hundred percent. That is true

But if we dig just a little deeper we see with the older pill is about .014%

Whereas with the new pill it was about .028%, which hardly seems worthy of a breaking news alert

But articles were posted about this misleading statistic and as a result naturally tens to hundreds of thousands of women stopped taking this birth control

pill

fast forward one year and that scare was blamed for

13,000 unwanted pregnancies many of which were teenage pregnancies... a lot of teenage pregnancy stories in this video... moving on

Do you guys actually know head lice is good for your health?

Seems pretty stupid

Right, but people actually thought this at one point and that brings us to the part of this video titled correlation or causation

or both

Remember, it's usually very easy to determine that two things are correlated from a statistical test but causation is a completely different thing

That isn't so easy to spot. yet

People are very quick to assume that A causes B just because A is correlated to B

Sometimes the logic can be stupidly obvious like fast-moving wind turbines are positively correlated to fast wind. As one goes up

The other goes up, but does that mean that fast-moving wind turbines cause fast wind?

Well, obviously not it's the other way around

But in many cases it isn't this obvious like what if I said that kids who watch more violent TV shows are more violent themselves

Does this mean that those shows cause kids to be more violent?

I mean that could be possible and definitely would be an immediate thought for many people

But what if kids who are more violent just happen to watch more violent TV shows that also seems perfectly reasonable

So we can't just jump to conclusions too early

Even though that's what many people would probably do. Or in the Middle Ages European

Saw that people who had head lice were normally healthy. Whereas people who were sick rarely ever had head lice. as a result

They assumed that lice would cause people to be more healthy when in reality head lice is very sensitive the body temperature

So people had a fever or anything like that the head lice would find another host

Then on the subject we have the third cause fallacy where two correlated events

Actually, don't cause each other at all, but it's rather a third thing causing both. For example ice cream sales

Do not cause an increase in heat strokes nor the other way around

Even though they are correlated. Hot weather is instead the cause of both of them. Or for the past several decades

Atmospheric co2 has increased along with obesity levels. So does one cause the other

Well, no richer populations tend to eat more and also produce more co2

And sometimes it can just be really unclear what's causing what.

Like a while back they found that students who smoke cigarettes get lower grades and that could mean smoking causes lower grades

Or maybe it means that getting bad grades causes smoking... Maybe the added stress that comes along with lower grades

Increases the chance that a student will pick up that first cigarette. That also seems like a reasonable explanation

Or it could be a variety of third factors is actually responsible for both

So even when looking at a statistical test with accurate numbers, it's pretty crazy how far you can still be from the truth?

Next we have a story that will probably have people making assumptions really early in the 1970s

Someone noticed that Berkeley was accepting 44% of male applicants to their graduate school

But only 35% of female applicants. Now right there half the Internet's like well say no more...

But only 35% of female applicants

That was an actual unedited clip of everyone on the Internet

Now these numbers that we saw are true

But very misleading when you look at how male and female applicants applied to each program within the Graduate School the assumed bias

Not only goes away but kind of flips. Look closely here in this row

You see there was a high acceptance rate for the program

In fact women had a much higher acceptance rate, but still overall it was high for everyone

however way more men applied to this one

Whereas more women applied to these programs down here with much lower acceptance rates

So since a higher percentage of women were applying to these programs with higher rejection rates

The overall acceptance of women would be lower guaranteed even though they are in fact slightly favored across a couple of departments

so either of these headlines could be published with the necessary stats to back them up and

All you gotta do is pick which one you want to use

toss

the other

Throw that into an article put it in bold right on the top, put the cleverly selected statistics down below it to back it up,

And you've got yourself a story

This here was an example of Simpsons paradox

Where looking at data as a whole tells a totally different story than grouping the data appropriately which I'm sure many of

You know, but I had to include it here

You guys remember the story of the blonde woman who robbed the elderly lady

Well, like I said, this is a famous case but not for the use of statistics

But rather the misuse of statistics in the courtroom, this was a classic example of the prosecutors fallacy

now this fallacy comes up when people assume that the probability of A given B is the same as the probability of B given A

Which I'm sure many of you know is not usually true from this equation.

Like if I said behind this curtain is an animal with four legs, that's the given. What is the chance that it's a dog?

Well, you probably do some thinking like well, it could be a dog, it could be a cat, it could be a cheetah

It could be a lot of other things and if you had to come up with a number you might say one in a hundred

One in a thousand or whatever, but if instead I said behind this curtain is a dog

That's the given, what's the chance that it has four legs?

Well, that's almost a guarantee because most dogs have four legs

So you see switch the given and the question at hand and the probability can change by a lot

So now let's look at what I said earlier

Turns out there was less than a 1 and 12 million chance that this random couple who just happened to fit all those descriptions

Was innocent, so the jury returned a guilty verdict.

This here was wrong

The stats actually showed us that given an innocent couple the odds that they fit the descriptions was one in 12 million

But then I said what the jury had also assumed that if you switch the given and the question at hand

The probability stays the same which we just saw can be very wrong

This left side should make sense like if I just grabbed a random couple out of a mall

That's the given there was a very small chance all of these would apply to them

But this is the false assumption that is the prosecutors fallacy

We're told or given

Hey

Here's a couple that fits all those descriptions. If maybe ten people in the entire city fit all of those given a random one

There's a 1 out of 10 chance that they're guilty or a 9 in 10 chance of being innocent. Not one in 12 million.

And remember Sally Clark who was found guilty of murdering her two children

This is also a famous case of the misuse of statistics

It turns out bacterial tests had actually been withheld that would reveal more specific information than a simple multiplication of two probabilities

Which didn't tell the full story at all.

Like it assumed that the two events were independent of each other when genetic or environmental factors could have definitely been at play

Like I said, sally was found guilty and sentenced to life in prison

But she only served three years when the convictions were finally overturned in early 2003. Up until then though

Sally Clark was widely criticized in the press as a child murderer

And she was never able to recover mentally from the false accusation. A few years after her release

She developed psychiatric problems and died in her home from alcohol poisoning in 2007

I'm gonna repeat that for everyone who didn't follow it. A woman lost two of her children due to natural causes

was accused of murdering them, was put on trial and found guilty due to a misuse of

Statistics, spent 3 years in prison, and even after her release was not able to recover mentally and died

Just about four years later

If you guys don't find that story

Insane then I don't know what to tell you

And actually the result of this case prompted the Attorney General to order a review of hundreds of other similar cases

Now because I don't want that to be where we end this video

Let's look at one more classic misuse of Statistics

This one has to do with how data is represented and it often involves bar graphs that don't have zero as their baseline

For example FoxNews one showed a chart detailing the numbers what would happen if the Bush tax cuts expired?

Do you guys see a problem?

Yeah

It starts at 34 percent at the bottom making a not even 15 percent increase look like a few hundred percent in

Reality the chart should look like this

Or take the Terri Schiavo case that occurred about two decades ago

Which involved a debate of whether a feeding tube should be removed from a woman in an irreversible vegetative state

During that time CNN posted this graph detailing which political parties agreed with the courts

It seems like Democrats supported the decision significantly more but because the baseline is not zero

It appears way different than it should, this is what the actual graph would look like

Or in 2015 the White House published a tweet about the increase in students receiving high school diplomas with an extremely misleading graphic

They made around a ten percent increase look like nearly 200%. Or in music

There was a chart released showing views between top artists that made drake look like he was ahead by a large margin

When in fact it was about a five percent lead

Now I'm guessing the comments on this video will be rather interesting

But remember these were cherry-picked events and it's not like everything. I said paints the full picture either

I just find it interesting that these numbers can change the way we think about a person

They can peek into some of the most intimate moments of our lives based on our grocery list

They can make very trivial events seem very serious and vice versa

You don't even need use wrong numbers for this

But hopefully this show just how not cut and dry math and statistics can be in the real world outside of a school setting

Especially and with that I'm gonna end that video there if you guys enjoyed be sure to LIKE and subscribe

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