I have a sweater that I’ve loved to death (if you’ve encountered me anytime in the last 5 years, you’ve probably seen it) and after many frustrating attempts to replace it with something similar, I took to eBay to try to find an exact replacement. This is something I’ve had success with in the past– put in some information about the item, and make a saved search that emails me every day with newly-listed results. But I’ve learned that eBay sellers only know about the mean, and not about variation.
Part of the problem is one of classification– eBay provides the standard six colors (primary and secondary), and a few descriptors like beige, ivory and brown, but probably the best description of the sweater above is “Multi-Color” which doesn’t really capture it. Probably eBay should provide a “Black and White” option.
What I think is funny about this example is that the seller is partially right– the typical color of this sweater is gray. But I’m not interested just in the typical color. I’m looking for a sweater with limited color variation (consistency across the garment). I’m looking for a unimodal color distribution with a small standard deviation, not a bimodal one!
This is abusing terminology a bit, but I think it illustrates an important point about how we don’t always care about the typical value, and when we talk about distributions (in any sense) we also need to take into account the variability.