Lesson 3 Be a Critical Thinker
Tricks behind statistics
In today's ____, there is a lot of statistical information around us all the time.
Every time we read an article on the Internet or see a commercial on TV, we are likely to come into contact with numbers and ____.
____, these numbers help us make better decisions in our daily lives.
For example, when we choose which movie to see, we can check the ratings and ____ the reviews of thousands of viewers.
Similarly, when people see ____ that show fastening a seat belt greatly increases the chances of surviving a car accident, they may choose to wear one themselves.
These are just a few examples of how statistical information plays an important role in our ____.
However, is it ____ to believe statistics exactly the way they are presented to us?
Unfortunately, statistics can be misused in ____ ways.
Let's learn about some common ____ behind statistics.
Samples: How Many and Who?
On the Internet, Minjeong sees an advertisement that reads, “100% of ____ report brighter and softer skin with Blossom Company's liquid facial soap.”
It claims that ____ results are from an independent laboratory and are guaranteed by a public agency.
____ does not question the statistics and buys some bottles, despite the high price.
____, although Minjeong uses the soap for a few months, she does not experience any noticeable changes.
Did Minjeong ____ happen to buy a defective product?
Or was the advertisement ____ fake?
When Minjeong read “100% of users,” she should ____ asked herself, “Where did the company get this figure?”
If Minjeong had read the tiny letters at the bottom of the ad, she would have found that the sample included only ____ people.
As in this case, when a sample is not large enough to ____ a wide range of results, it can be misleading.
By using small samples, companies can come up with any results they ____ and use them for their own purposes.
People can also get the ____ idea from statistics when a sample is not random.
For example, a restaurant may put survey ____ on the tables, hoping to know what most customers think about its food, service, or atmosphere.
However, few cards will be filled ____ by normal customers, because they don't have any reason to do so.
Only those with strongly positive or negative ____ are likely to respond to the survey.
This method of choosing a ____ is called “voluntary response sampling.”
Such samples are biased in ____ of strong opinions and underrepresent the moderate ones.
Therefore, when ____ see a statistic, remember that the sample is just as important as the statistic itself.
How many people were in the ____? Who were they?
If you don't know, be careful not to leap to ____.
The Trap of Averages
ABC Corporation wants to hire ____ employees.
In order to look ____ a well-paying company and to recruit competent candidates,
the company decides to distribute a press release that says the average yearly salary of its employees is $57,000, which is ____ high.
However, the fact is that more ____ half of its employees earn no more than $30,000 or less a year,
and the most common salary for employees is only ____
____ the company spread false information? How is this possible?
It's because the ____ used the trap of averages.
Averages ____ show different pictures depending on which type is chosen.
To understand the meaning of different types of ____, let's look at the illustration on the next page.
Most often, the term “average” ____ the “mean.”
It is calculated by adding all the values in a group and ____ the result by the number of group members.
However, the mean is not the only kind of ____.
There are two more kinds: the “median” and the “____.”
The median is the ____ that is exactly in the middle of all the other figures.
In this case it is $30,000, because 12 employees are making more than $30,000 and 12 are ____ less.
The mode is the number that appears most frequently—$20,000 in this ____.
As you can see in the illustration, there are only a handful of people that are ____ an average salary of $57,000 or higher.
However, because the company wanted to be perceived as a well-paying one, it used the ____, which results in a deceptively high average salary.
An average is convincing because it is so ____.
To avoid being tricked, however, you have to ____ what sort of average is being reported.
You also need to find out the distribution of the values in order to ____ a more accurate idea of the real data.
Same Data, Different Graphs
In ____ media, graphs are often used because they display data more efficiently than tables of raw data do.
However, graphs can be misleading, too. ____ look at the two graphs below.
The two graphs shown here illustrate how ____ can be misrepresented.
In the first graph, the vertical axis ____ all the way up to 100 and all the way down to 0, which makes the decrease in the percentage look modest.
In the other graph, only 10 percentage ____ are shown, from 65 to 75, which makes the change seem much more extreme.
____ is the fact that the two graphs are based on exactly the same data.
So, if you want to point out the seriousness of skipping breakfast, you ____ use the second graph.
In fact, you can make nearly any graph more convincing in favor of your argument by cutting off the graph at a certain ____.
Hence, whenever you see a graph, you should check the units on the vertical and horizontal axes to see what the ____ and lowest values are.
Don't simply assume the visual impact is the same as the ____ story.
Check whether the graph is presented in a ____ way to emphasize a point.
Look with a Critical Eye
When people state opinions in articles, speeches, debates, or advertisements, they often give some ____ to support or reinforce their point.
If these statistics are found through proper research methods, then they are ____ facts.
However, many statistics that you see and hear could just be numbers that are meant to convince you of a certain ____.
Therefore, the next time you come across some statistics, don't ____ accept any data that is presented.
Look at the statistics in detail with a critical ____, and then judge whether or not they are convincing.