# How many people will be in the top 10% in at least one examinations

• MHB
• Tomacork
In summary, when 100 people take two exams, with a correlation of .6, we would expect 19 people to be in the top 10% in at least one exam. However, if the exams were unrelated, we would expect only one person to be in the top 10% for both exams. For more than two exams with different correlations, the calculation would be more complex and would depend on the specific correlations between each exam. In the example given, with three exams (A, B, and C) correlating at .7, .6, and .5 respectively, it would require further analysis to determine the number of people in the top 10% for each exam.
Tomacork
If 100 people take two exams, the results of which correlate at .6, how many people will be in the top 10% in at least one examinations? I understand that if the exams were unrelated then we would expect one person to be in the top 10% for both groups,and therefore 19 people would be in in the top 10% in at least one exam. However, I don't know how to calculate this when the exams are correlated, nor how to calculate it if there is more than 2 examinations. Any help appreciated

There will be, of course, 10% of 100= 10 people in the "top 10%" of each exam. If the tests "correlate at 0.6" we would expect 0.6 (10)= 6 people to be in the top 10% in both exams.

HallsofIvy said:
There will be, of course, 10% of 100= 10 people in the "top 10%" of each exam. If the tests "correlate at 0.6" we would expect 0.6 (10)= 6 people to be in the top 10% in both exams.

Thanks for that. It is simpler than I thought. I thought that the correlation between the examinations would need to be squared. How would I calculate this for more than 2 exams and with different correlations? For instance, how many people would be in the top 10% in three tests(A, B & C) which correlate at .7 for A/C, .6 for A/B and .5 for B/C?

## 1. How is the top 10% determined in examinations?

The top 10% in examinations is determined by ranking the scores of all the test takers and selecting the highest 10% of scores.

## 2. Is being in the top 10% in at least one examination a good indicator of academic success?

Being in the top 10% in at least one examination can be a good indicator of academic success, but it is not the only factor to consider. Other factors such as consistency, effort, and overall performance should also be taken into account.

## 3. Is it possible for more than 10% of test takers to be in the top 10% in at least one examination?

No, by definition, only 10% of test takers can be in the top 10% in at least one examination. This is because the top 10% is determined by ranking the scores and selecting the highest 10%.

## 4. Are there any specific factors that contribute to being in the top 10% in at least one examination?

There is no one specific factor that guarantees being in the top 10% in at least one examination. It is a combination of factors such as intelligence, hard work, and effective study habits that contribute to academic success.

## 5. How can being in the top 10% in at least one examination benefit an individual?

Being in the top 10% in at least one examination can benefit an individual by increasing their chances of getting into a prestigious university, obtaining scholarships, and standing out in job applications. It can also boost their self-confidence and motivation to continue striving for academic success.

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