The Existence of Average

More than once the question has come to my mind: Would it be better to live in a world with extreme highs and lows or a world in which you have the average of the two? Theoretically thinking, wouldn't both have the same effect? Theoretically, [in the world of highs and lows] the highs balance out the lows and you are given the effect of average anyway. However, the effect in the two worlds is different. My thought is this: A high plus a low does not equal an average. Our lives are not math. Two opposite experiences do not leave you with nothing.
Say you find one hundred dollars one day. You tell people about it. You wonder what you should do with the money. You muse on what you could buy with that money. You take another look in your wallet and somehow you have lost the hundred dollar bill. It must do that a lot. Are you the same as if you had not found the money at all? Theoretically, yes. But you really aren't. You are changed from the experience. You have a funny little anecdote to share with people about luck. You've thought about your values (where you put your money). You have another little thing taking up a piece of your allotted memory.
Bad experiences develop character and appreciation. Good experiences drive us to keep living. Average experiences create a comparison to differentiate between the two. If your whole life were average, a comparison to nothing, would your life be anything at all?