Skill Level Appropriate for all
- [Instructor] I've taught a lot of college classes, and a lot of college students. Things I've discovered. Students generally dislike exams. If it makes you feel any better, teachers dislike writing them, almost more than grading them. And, then there's the griping that follows. In most classes students see two scores, their individual score and the classes overall average score. Simple stats, one data point versus one type of center for the data.
Average is calculated by adding up all the individual student test scores and dividing them by the number of students. In many cases, struggling students like to point to the average as evidence that the exam was too difficult. Good and great students alike, will also tend to agree with this observation. Everybody wants a curve. Look, sometimes exams are difficult, but sometimes the average isn't the best way to look at the data. Suppose we had 25 students and these were the exam scores, the average is 69.4%.
But, by arranging the data you can see that most students did pretty well. Five totally bombed the exam. These data points are referred to as outliers. But 20 students got respectable scores between 60 and 100. When you have a few extreme outliers, the average doesn't provide a very good snapshot of the class. That's called skewing the data. So, one stat alone cannot tell the story. We need a group of statistics to provide a more detailed view.
The median is another type of middle. 25 test scores, line them up one to 25, in order, from lowest score to highest score. The middle score, number 13, 75%. Over half the students got 75% or above. The mode, that's another metric. The most popular test score. Four students got an 85%. Pictures help too.
Here's a distribution of the data. Looks like some students understood very well, but a few just had no clue. None of this means the test was hard, and it doesn't prove it was easy. Instead, it allows us to ask good questions. It helps us to find important answers. I'm a university instructor, the exam is a test for the students, but the exam data is the test for the instructor. This is the data I work with, not purely just to measure, but also to discover and improve.
Get a grasp on statistics foundations, and let the data in your workplace lead you to interesting questions and important answers.