While I agree with the spirit of this, the conclusion is not necessarily correct. The mean can be highly informative, but should never be used alone.
Assume you know only the mean revenue and the maximum revenue (but forgot to measure variance). You could make an extreme scenario with the maximum possible variance to generate a "worst case" distribution. In this scenario, all customers either provide zero revenue or the maximum. This distribution has the maximum possible variance for a given mean and maximum.
Will you be profitable this year? Your chances will be better than the worst case scenario described above! If higher moments are known (variance, skew, etc.), more accurate bounds can be found.
In conclusion, the mean can be very useful, especially if higher moments are known.
Assume you know only the mean revenue and the maximum revenue (but forgot to measure variance). You could make an extreme scenario with the maximum possible variance to generate a "worst case" distribution. In this scenario, all customers either provide zero revenue or the maximum. This distribution has the maximum possible variance for a given mean and maximum.
Will you be profitable this year? Your chances will be better than the worst case scenario described above! If higher moments are known (variance, skew, etc.), more accurate bounds can be found.
In conclusion, the mean can be very useful, especially if higher moments are known.