annualized return example, return, remember, compound, only

DoubleDip

I remember when we get annualized return
only need to compound each period's return
for example quater 1-4 return is 1% 1% 2% 2% we only need to 1.01 x1.01x1.02x1.02
but in book 5 p120 EOC12 they calculate annualized return as (1.01 x1.01x1.02x1.02)>(1/4) x 4 is there any inconsistency here?
I remember in evaluation ,we also only need to compound each period's return