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