Ok, so I read in a lotta places that the average yearly return of the stock market was like 10%-11% for the past 75 years or so. How is that average calculated?

Consider the case where you have a $100 invested for two years. First year you lose 50% and second year gain 60%. This is a 10% average, but instead of having $121 you only have $80 which was actually a 20% decrease total.

If you gain 100% first year and lose 90% the second year, you only have $20 left...

If you gain 15% first year and gain 5% the second year, you have $120.75, etc...

The above cases had a 10% average yearly return but they didn't end up with $121 at the end of the two years. I hope this 10%-11% average was calculated in some other way than adding up all the yearly returns and dividing by the number of years.

EDIT: One more question. When someone says "If you had $x invested in ... 70 years ago it would have grown to $y now". Do they actually mean it or do they just see the average return over 70 years and plug the numbers in their calculators?