# What method in statistics would I use to show how a student taking 2 different exams in to different subjects, a 50% on one and a 80% on the other....what concept could be applied that the 50% is...

What method in statistics would I use to show how a student taking 2 different exams in to different subjects, a 50% on one and a 80% on the other....what concept could be applied that the 50% is actually better than the 80%???

embizze | High School Teacher | (Level 1) Educator Emeritus

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A student taking 2 different exams in 2 subjects received a 50% on one test and an 80% on the other. How could the 50% represent a better result than the 80%?

It all depends on the mean and the standard deviation of the tests.

For example: suppose that there were 100 students in each class.

In the class that the student received a 50% (class A), the mean score was 48% with a standard deviation of 2%.

In the class that the student scored an 80%(class B), the mean score was 85% with a standard deviation of 5%.

In class A, assuming the scores were normally distributed, the student scored better than 84% of her classmates. (The z-score is `z=(50-48)/2=1` and the area to the left of a z=1 under the standard normal curve (found in a table or using technology) is 84%)

In class B, assuming the scores are normally distributed, the student , the student scored better than only 16% of the other students.

So the score of 50% is "better" than the score of 80%.