Both measures of central tendency and variance can be used for decision making. But variance or the spread is more trusted upon especially in life line industries like automobile,aerospace and medical equipments . It's because variance takes a call on each data point which is very crucial especially for the above mentioned industries. Unlike central tendency, It never generalizes a set of data points.Infact it uses central tendency as a reference to assess each data point and arrives at a spread that the process or the product is capable of.
Central tendency can be misleading at times. Let me quote one example I studied during my BB course in Benchmark.A decision has to be taken on whether the newly appointed cricket coach can continue in his job or not. A survey has to be taken. Cricket coach needs to get a minimum 25 percent vote to continue in his job.Off 2000 people 482 support the coach.This ends up at 24.10 percent which might go against the coach.But if we run a 1 proportion hypothesis test to check if the support has truly gone below 25 percent, it gives us more light on the support and goes in favour of the new coach. It doesn't merely go by division of numbers but takes other factors like confidence level, p value into consideration.
If we want to regulate things like controlling speed of a car. We establish a monitoring mechanism where a car can go as slow as x km/hr or go as fast as y km/hr. Any deviations or variations beyond the levels by any car will be tracked and reported through a device.