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“When looking at the overall entrance test data for Unseen University for the year 2014-15 it...

“When looking at the overall entrance test data for Unseen University for the year 2014-15 it was found that the proportion of female students who cleared the test was smaller than the proportion of male students who cleared the test. But when the data was broken up by department it was found that in every department the proportion of female students who cleared the test was larger than the proportion of male students who cleared the test”. Is this scenario arithmetically possible? Explain.

Math   Statistics-And-Probability   
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Answer #1

This scenario is not arithmetically possible. It is given that in Every department, the female proportion is higher than males. Assume for teh moment taht there are only two departments and in each department, teh female proportion is more. This clearly indiactes that when we add up, the total female proportion has to be higher. Therefore a University will definetly there are more departments, the higher numbers will add up more and that's why, it is not arithmetically possible.

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