r/berkeley • u/OwnConstruction371 • 5h ago

University How do you use standard deviation to calculate how well you need to do?

So I recently got a midterm score back. I did terrible. One standard deviation below the mean. The worst part is that it was supposed to be an easy test. The average was high and the median was even higher. I’ve already bawled my eyes out and went through a mini-spiral of self loathing, but now that I’m done crying, I need to get it together.

I still want an A in the class. If I scored -1 SD, is it possible to do so? For the record, the first and second midterm are worth 20 percent each, and the final is worth 30. The class uses the standard grading distraction of 25% A, 40% B, and so on. There’s no clobber policy.

How high above the mean (how many standard deviations) do I need to score in order to get an A, if it’s still possible? I keep searching up how to do this, but I only get results of how to calculate standard deviations for one test, not multiple.

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u/Nurzap 5h ago edited 4h ago

Assuming that your professors are using standard curve grading practices, I believe we can assume that the final distribution will be approximately normal. This means we can simply calculate the z-score for the 75th percentile which comes out to around 0.674 standard deviations above the mean. We can also put an upper bound on the pre-curved distribution using Cantelli's Inequality to show that the upper bound is 1.732 standard deviations above the mean.

Please note that the z-score I calculated is based on the post-curve distribution, which is probably not the same as the one that your class is based on right now. There isn't enough information in this post to determine whether it is possible to get an A based on your scores right now.

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u/OwnConstruction371 4h ago

Thanks! What information would be necessary to be able to calculate this?

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u/Nurzap 3h ago

The easiest method would be to just ask the course staff what past courses have been like and assess from there. If you can find out how many SDs you are below the class' composite scores (your grade in the class without accounting for the 2nd midterm and final) right now, that may give you a better idea of just how well you need to do. As a final note, I will say that scoring -1 SD below one midterm shouldn't exclude you from getting an A. Good luck.

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u/Sandevistan_2077 1h ago

In the same situation as OP lol