Problem With Averages

If a 4.5 feet person (who does not know swimming) is to cross a river which at its banks is 2 feet deep, and in the middle 6 feet deep.
If he is to consider the average depth, then it would turn out to be 4 feet deep. So as the person is 4.5 feet, and if he crosses the river just because it has an average depth of 4 feet, he would drown when he reaches the middle of the river. This is the problem with the averages. It usually hides the real scenario and it is usually difficult to determine anything properly by using averages. Thus it becomes very important to use variation and targets instead of averages while doing Quantitative Project Management. One example where I can think of where average is used considerably well and across many organizations is the Customer Satisfaction Survey (CSS). With the known issue of averages, what would be the best way to determine the CSS?