I was reminded of this at a beer tasting I went to a number of years ago. The host of the evening was a former brewer who recounted a tale about Budweiser overnight air freighting a cargo of hops to the UK because the brewery there had run out. Instead of using a similar type of local hops the company decided it was more important to ensure absolute consistency and so delayed the brewing process and arranged for the right hops to be delivered at great expense. Presumably they felt that the potential damage to their brand of a slightly different tasting brew was far greater than the cost associated with the last minute transportation of the proper ingredients. It could be argued that here too consistency was considered more important than quality (sorry Budweiser fans). This is perhaps an under utilized concept. We strive for a high average in lots of situations where a low variability might instead be a viable option.
In other situations, high variability is under appreciated. Consider the standard UK driving test. Since there is no real penalty for a failed driving test (bar the cost and inconvenience of rearranging the test) then a possible strategy is to employ a high-variability driving standard. Chances are good that a high variability approach will soon lead to a driving test that passes the muster, even if the average driving quality is below standard (not so high variability that you crash the car obviously but you get the idea).
Another, example would be in matchplay golf. I am no expert here, but essentially, in matchplay, two golfers play a round of golf and instead of counting overall strokes for the entire round, a player will score a point if they take fewer strokes on a given hole than their opponent. If they each take the same number, they each get half a point. This encourages riskier play (i.e. high variability). since there is no greater penalty for losing badly (e.g. by 10 strokes) than for barely losing (e.g. by one stroke). An opponent who either birdies, pars or triple bogeys every hole with equal probability would likely tie with an opponent who pars them all, despite taking more shots overall.
Another situation where the variability is arguably more important than the average is on the ratings website Trip Advisor. Imagine if restaurant goers were more likely to post a Trip Advisor report if they are either unusually satisfied or unusually dissatisfied, and were unlikely to do so if they lay somewhere in the middle. Under this scenario, avoiding variability in one direction (i.e. really poor service), but promoting it in the other (i.e. occasionally raising the standard of service above the norm) could result in a Trip Advisor score in excess of the average quality.
In a vaguely related situation, you might be familiar with the British TV quiz show Pointless. It is a magnificently sedate and entertaining affair, but the central premise is that the producers ask 100 members of the public questions and give them 100 seconds to answer. Typical questions have multiple answers, such as naming top ten ranked male tennis players between specified years or naming countries with a certain colour on their flag. Contestants on the show are then asked the same question and must give a correct answer that the fewest people said.
What isn’t revealed is whether the 100 members of the public are allowed to get them wrong. If a contestant guesses incorrectly they pay an immediate penalty of 100 points. If one member of the public guesses incorrectly there is presumably no penalty at all. So, to take the colours on national flags example, a member of the public might simply spend their 100 seconds naming every single country they can remember regardless of whether they know what colours are presented on its flag.
More subtly, they might be more willing to take a chance on a country they aren’t sure about than a contestant can afford to be. In this situation, members of the public can answer with great variability and potentially get more obscure correct answers (along with a lot of very wrong answers). Meanwhile the contestants must pick and choose very carefully. If the public had to play by similar rules, where they were stopped from providing answers after their first wrong answer the scores on Pointless might be a lot lower (and I would argue fairer).
Variability then is a fickle beast and while we regularly think of it as hiding the truth or as a nuisance factor, without it there would no need for statistics at all and that, we can all agree, would be a terrible situation!