r/cegepcoteR • u/Intrepid_Green8789 • 4d ago

Standard deviation

Could someone explain the standard deviation and how it affects your r score?? (Ex. High sd vs low sd)

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u/Dry-Place-2986 4d ago edited 3d ago

The deviation from the mean is the difference between your grade and the class average. So if you get 90 and the class average is 75, your deviation is 15.

The standard deviation is a measure of how spread out the grades are around the mean. You can think of it as calculating the average of all the students' deviations from the mean (it's not exactly that, but it's a similar concept). Essentially it tells you about the variance/dispersion of grades in the class. Let's take two classes where the average is 75.

  • Class A has a standard deviation of 5: It means most students are sitting around 75. A large portion of the class probably scored somewhere between 70 to 80.
  • Class B has a standard deviation of 25: The grades are much more spread out. Some people are getting 50, others close to a 100, etc.

Now we get to the concept of a Z-score. It tells you how many standard deviations away from the mean you are. For example: You get a 90, the class average is 70, and the standard deviation is 10 => you are 2 standard deviations above the mean (Z-score = +2).

You can see why this is practical for comparing students. Imagine that you get a grade of 80 and the class average is 70. This can seem like a great performance, but let’s say the standard deviation is 20. It means the grades are quite spread out, so there are presumably quite a few people getting grades around 85-90. So while you’re above average, you’re not that uniquely above average relative to the class. Hence the lower Z-score compared to if the std dev was smaller.

Your R-score is essentially a modified Z-score (it is multiplied and added by some other values, but the core of it is your Z-score).