Are males smarter or dumber than females? It depends on how you normalize the IQ test.
Normalizing of IQ tests is what most people completely forget in discussions of male-female difference.
Men have an IQ test advantage in math and spatial relations, women have an advantage in written language. In both cases the advantages are significant enough to result in measurable differences on an IQ test.
Consequently IQ testing is normalized for white males and females at 100*. The tests are set to make white males equal to females. If the questions in all parts of the IQ test were held equal males would get higher scores than 100 resulting from a large number of math and spatial relations questions, vice versa for the results for females on language questions if language questions were dominant.
Just think, the female professors at Harvard drove out the president of Harvard over ignorance of this issue and gave him back to America as head of the Economic Council. (Actually the issue was only about math scores at the extreme end of the statistical curve, 6 sigma.)
*Note the use of the term white. If tests were normalized for ethnicity, whites would be inferior (averaging 90 IQ) to Japanese and whites would be superior to some others.