Tom, that's not what average means. It just isn't. The word average has a specific meaning.
The word 'average' in no way implies even slightly anything about the distribution within the group for which the average is being taken. The distribution within each group can very easily be (and often is) far bigger than the difference between the averages of each group.
E.g. take height, as it's more visible. If you measure 100 men, they will have many different heights. One man will be the tallest, one will be the shortest, and the rest in between. You can find the average height (we can use the most common kind of average which is a 'mean' = add all their heights and divide by the number of men).
Do the same for 100 women. A lot of the women will be taller than a lot of the men. But the average height for the male group will be bigger than the average height for the female group. And in the case of height, this difference will not be as big as the difference between the tallest and shortest man, but there will be a difference.
Or line up all 200 people by height from shortest to tallest. The men and women will be all mixed up with men and women at both ends of the line. But at the front of the line will be lots of women and fewer men, and at the end of the line will be lots of men and very few women.
That's the thing about statistics. They apply to groups. They don't have any meaning applied to individuals. Otherwise you would be 49% male, 1/3 chinese, etc...
So no, if you're being very very precise, you're right that the statement 'men are stronger than women' is not true, as it's not true in every case (though it's true in more cases than it's untrue, but still, it's often untrue). However, 'MOST men are stronger than MOST women' is true, and 'the AVERAGE man is stronger than the AVERAGE woman' is true.
If you use average in the sense of mean (add all there heights up and divide by the number of men), you end up with a figure that is not always very helpful. A good example is the average temperature of a region. If we add up all the daily temperatures within a year and divide them by the number of days you will end up for my region with a figure like 12 degree Celsius. Although this figure is absolutely correct, it is also a tautology. But if someone tells me that the temperature on average (meaning not counting the extremes) fluctuates in a year between -10 and + 35 Celsius I get a better idea. And if it is a little bit more specified like; in the summer it is on average between +15 and +35 Celsius, then I can safely conclude it is a good temperature to go out camping. With a more "correct" average of 12 C. I can not come to the same conclusion.
So it is not just a matter of the meaning of the word average, it is also about the kind of information that you are looking for. In the scientific tests they chose deliberately not to look at the mean figure. As that did not provide them with the information they were looking for.