This is not one question, but several. First, is it true that a woman's brain is smaller than that of a man. The answer is yes, scientists say that not even 80, but about 125 grams, if the average for the planet.
Second, does this mean that any woman will have a smaller brain than any man. The answer is of course not, this value varies quite a lot.
The third is whether intelligence depends on the size of the brain. The answer is not really. Not only are we not yet sure what intelligence is at all, but in general it is now accepted to think that cognitive abilities depend not so much on brain mass as on the "encephalization coefficient" - the ratio of brain mass to whole body mass. And men, again on average, are heavier than women and this ratio is higher for women.
In addition, the brain does not consist of intelligence alone, whatever is meant by this word. Men and women have different brain lobes developed in different ways. On average, men have more gray matter in some areas of the brain, women in others. It is not known which of them influence this intelligence more.
There is such a TED lecture. Neuroscientist Catherine Vidal talks about whether the brain has sex differences. https://youtu.be/lkNF8rYkTTk
In 1861, Paul Broca actually calculated the average difference in the brains of a man and a woman, and it was 150 grams. With an initial weight of 1350 male brains and 1200 female brains. I also want to note that he was an ardent supporter of the theory that men had more brains than women, white people more than blacks, and bosses more than their subordinates. p>
But today we know that there is no connection between the size / weight of the brain and the intelligence of its owner. We know about this thanks to some men who donated their brains for the benefit of science. For example, Anatole France's brain weighed 1kg, Turgenev's 2kg, and Einstein's brain weighed only 1250g.
In fact, the level of intelligence depends on the density of synoptic connections in the human brain. And even a 1kg difference in brain weight will not solve anything, since synoptic plasticity can more than equalize this difference.