How many female students are in the excellent performance category?

Concept

In a two-way table, each row total and column total equals the sum of its cells. A stated percentage can be used to obtain the grand total, after which missing cells can be found by subtraction.

Application

1. Let T be the total number of students. Since 40% of the students are female and the female total is 32, 0.40T = 32, so T = 80.

2. Half the students are either good or excellent, so good + excellent = 80/2 = 40.

3. The good column total is 30, so the excellent column total is 40 - 30 = 10.

4. The male-excellent cell already contains 10. Therefore female-excellent = total excellent - male excellent = 10 - 10 = 0.

5. Hence, the number of female students in the excellent category is 0.

Cross-check

The completed excellent column is 10 + 0 = 10, and good + excellent is 30 + 10 = 40, exactly half of the total 80.