Approximately, what proportion of good students are male ?

Concept

In a two-way table with r rows and c columns, the row totals, the column totals and the grand total still leave (r − 1) × (c − 1) interior cells free, so the marginal totals on their own never pin the table down. Every extra independent fact — a cell that survived, or a stated fraction of one row or of the whole group — removes one of those degrees of freedom. So convert each quoted percentage or fraction into an absolute count first, check that the extra facts are as many as the free cells, and only then propagate everything along the rows and columns by subtraction until each empty cell is forced.

Applying it here

1. Here the table has 2 gender rows and 3 performance columns, so even with every total known (2 − 1) × (3 − 1) = 2 interior cells stay free; the surviving Male–Excellent entry and condition (c) supply exactly the two independent facts needed to close it.

2. Females number 32 and make up 40% of the students, so the grand total is 32 divided by 0.40, that is 80 students.

3. Males therefore number 80 minus 32, that is 48 students.

4. One-third of the male students were average, so the Male–Average cell is 48 divided by 3, that is 16.

5. Half the students were excellent or good, so the Excellent and Good columns together hold 40 students and the Average column holds 80 minus 40, that is 40.

6. The Average column therefore gives Female–Average as 40 minus 16, that is 24.

7. The Good column total is 30, so the Excellent column total is 40 minus 30, that is 10; since the Male–Excellent cell already holds 10, Female–Excellent is 0.

8. The male row must add up to 48, so the Male–Good cell is 48 minus 16 minus 10, that is 22.

9. The share of the good students who are male is therefore 22 divided by 30, which is 0.733… and rounds to 0.73.

Cross-check

Filling in every cell and re-adding the table both ways confirms the reconstruction:

The female row adds to 24 plus 8 plus 0, that is 32 as given; the Good column adds to 22 plus 8, that is 30 as given; and the grand total is 48 plus 32, that is 80. Reading the same column the other way round gives 8 out of 30, about 0.27, which is the female share rather than the quantity the stem asks for.