Standard Score (as Used in Korea's College Entrance Exam)

Which is more impressive: climbing 100 meters up a small hill near your house, or climbing 80 meters up a harsh snowy mountain? The snowy mountain, of course. Test scores work the same way.

A 95 on an exam so easy that everyone got most questions right can actually be worth less than an 85 on an exam so hard that everyone struggled. The original score you earn on the paper is called the "raw score." If you compare raw scores alone, you ignore how hard the test was.

The problem gets even worse when students pick their own subjects. Ranking someone who chose an easy subject against someone who chose a hard one by raw score is unfair. That's why a common ruler was needed to even out the difficulty of each test.

Once you have a common ruler, you can compare results on the same basis no matter how tough the test was. But if the students taking each subject differ in ability, some advantage or disadvantage remains. So for the Korean language and math sections of the CSAT, scores in the elective subjects are adjusted once more using the common-subject scores before standard scores are assigned.

To build a standard score, you first need two key numbers. The first is the "average score," the center of all the test takers' ability. The second is the "standard deviation," which shows how widely scores are spread around that average.

Subtract the average from your raw score, then divide by the standard deviation. That tells you how far ahead of the average you are. In statistics, this is called a "Z-score." A Z-score sets the overall average at 0. If your score is above the average, it's positive. If it's below, it's negative.

But a report card full of negative numbers and decimals would be hard to read at a glance. So for exams like the CSAT, the average is moved to 100 points (50 for the inquiry subjects), and the Z-score is multiplied by a fixed number to dress it up as an easy-to-read positive whole number.

The converted score isn't just a count of correct answers. It works as an objective marker that tells you roughly where you stand among all the test takers.

On a brutally hard test, the so-called "fire exam," the average score of all test takers drops a lot. If you get a perfect score when the average has sunk to the floor, the gap from the average becomes huge. So the top standard score shoots up very high.

On the other hand, on a very easy "water exam," most students score high and the average gets very high. Even a perfect 100 is only a little above the average, so the top standard score ends up low.

How tightly the scores are bunched together also matters. The more students are packed closely in the middle ranks, the rarer, statistically, it is to break out of that crowd with a high score. So that achievement is rated higher.

So a high standard score doesn't simply mean you answered many questions correctly. It's a relative measure of how uniquely you stand out among the many competitors who took the same test.