In today's world, 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 figures. Generally, 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 see the reviews of thousands of viewers. Similarly, when people see statistics 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 lives. However, is it safe to believe statistics exactly the way they are presented to us? Unfortunately, statistics can be misused in many ways. Let's learn about some common tricks behind statistics.

On the Internet, Minjeong sees an advertisement that reads, "100% of users report brighter and softer skin with Blossom Company's liquid facial soap." It claims that these results are from an independent laboratory and are guaranteed by a public agency. Minjeong does not question the statistics and buys some bottles, despite the high price. However, although Minjeong uses the soap for a few months, she does not experience any noticeable changes. Did Minjeong just happen to buy a defective product? Or was the advertisement completely fake? When Minjeong read "100% of users," she should have 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 five people. As in this case, when a sample is not large enough to show a wide range of results, it can be misleading. By using small 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 not random. For example, a restaurant may put survey cards on the tables, hoping to know what most customers think about its food, service, or atmosphere. However, few cards will be filled out by normal customers, because they don't have any reason to do so. Only those with strongly positive or negative reactions are likely to respond to the survey. This method of choosing a sample is called "voluntary response sampling." Such samples are biased in favor of strong opinions and underrepresent the moderate ones. Therefore, when you see a statistic, remember that the sample is just as important as the statistic itself. How many people were in the sample? Who were they? If you don't know, be careful not to leap to conclusions.

ABC Corporation wants to hire some employees. In order to look like 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 quite high. However, the fact is that more than half of its employees earn no more than $30,000 or less a year, and the most common salary for employees is only $20,000. Did the company spread false information? How is this possible? It's because the company used the trap of averages. Averages can show different pictures depending on which type is chosen. To understand the meaning of different types of averages, let's look at the illustration on the next page.

Most often, the term "average" indicates the "mean." It is calculated by adding all the values in a group and dividing the result by the number of group members. However, the mean is not the only kind of average. There are two more kinds: the "median" and the "mode." The median is the number 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 making less. The mode is the number that appears most frequently—$20,000 in this case. As you can see in the illustration, there are only 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 used the mean, which results in a deceptively high average salary. An average is convincing because it is so simple. To avoid being 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 get a more accurate idea of the real data.

In mass media, graphs are often used because they display data more efficiently than tables of raw data do. However, graphs can be misleading, too. Let's look at the two graphs below. The two graphs shown here illustrate how data can be misrepresented. In the first graph, the vertical axis goes 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 points are shown, from 65 to 75, which makes the change seem much more extreme. Notable 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 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 certain point. Hence, whenever you see a graph, you should check the units on the vertical and horizontal axes to see what the highest and lowest values are. Don't simply assume the visual impact is the same as the real story. Check whether the graph is presented in a specific way to emphasize a point.

When people state 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 research methods, then they are objective facts. However, many statistics that you see and hear could just be numbers that are meant to convince you of a certain view. Therefore, the next time you come across some statistics, don't blindly accept any data that is presented. Look at the statistics in detail with a critical eye, and then judge whether or not they are convincing.