Test 1 scores

Here is some information on scores for test 1. It should be useful in interpreting your score.

First, some descriptive statistics:

mean = 29.21 out of 40 possible points (73.04%)
median = 29.5 (73.75%)
mode = 34 (85%)
standard deviation = 4.9 points (12.28%)

The mean is the average (sum all scores and divide by the number of observations). median is the middle score, found by sorting scores highest to lowest (or lowest to highest, doesn't matter) and finding the score in the middle (in the event of an even number of observations, take the middle two scores and find the average of those two scores). The mode is the most frequently occurring observation. These are all measures of "central tendency" or average (more broadly speaking than just the arithmetic mean). Ideally, these three measures should be close together. Certainly the mean and median are close, but in this case, the mode is very different. But for a few reasons (small sample size and the debatable assumption of "normality") the mode is probably not going to be a reliable statistic for our purposes.

The standard deviation is a measure of how the scores are distributed around the mean. The higher the number, the greater the dispersion.

My typical targets are a mean and median near 80%. So this test average is a bit low. That tells me that either the test was difficult or many people were not prepared. Or some combination of the two. Regardless, since every test is an independent event and that every newly created test has an inherent bias (this particularly applies to multiple-choice dominated tests), these statistics can assist me in figuring out how people did, correcting for the degree of difficulty.

So typically, I will take some measure of the middle (mean or median typically) as the break between the Bs and the Cs. Then going up one standard deviation from the mean, I can find a break between the As and the Bs. Similarly, I can go down one standard deviation from the mean to find the break between the Ds and Cs. Further, going down a second standard deviation from the mean I can find the break between the Ds and the Fs.

So, you can use the following scale as a guide for interpreting your score:

A: 34 and higher (5)
B: 29.5 to 33.5 (6)
C: 24.5 to 29 (7)
D: 19.5 to 24 (3)
F: 19 and below (0)

The number in parentheses is the frequency of observations in that range. So no one is in the F range. And the number of As and Bs is greater than the number of Cs and Ds.

But please take note: Letter grades are not recorded, only your score. Your score is weighted by the number of points on the test (40) and the weighting in your overall grade (20%). So the only letter grade you ever really get is the final grade for the course. Hence, I do not write a letter grade on your test. I just give you the raw score. But as you've seen here I've painstakingly tried to explain your score to you.

After the next test I'll give you an overall score for the course so far. It is fair that when there is a "curve" that you have some clear idea of how you are performing.

Good luck with the rest of the course.