2 min read

Oranges and lemons

One of the basic principles of applied statistics is that the data don’t tell you what the question is.  For example, the distribution of a variable doesn’t tell you what summary statistic you are interested in.

For mean vs median, a good example is binary variables. If a variable (like the indicator variable for dying in a car crash) is 0 for most people and 1 for a few people, the variable is very highly skewed but the mean (probability) is a much more useful summary statistic than the median (zero). For minimum or maximum it’s a bit harder. 

A few weeks ago I was in Melbourne, and in the discussions of weather that inevitably arise, I claimed Auckland had warmer winters. After returning to Auckland I started to doubt this. It’s kinda chilly here, still. [Y’all in Michigan can stop laughing now]

My reason for believing the winters were warmer in Melbourne was horticultural. There are plants you can easily grow in Auckland that can’t cope with Melbourne weather. In particular, lemons grow in any backyard, but oranges and grapefruit require well-chosen varieties and especially sunny locations to produce good fruit in Melbourne. In Auckland, you just stick them anywhere convenient. 

It turns out that the average minimum temperatures in Melbourne are lower than in Auckland, and the record minima are distinctly lower: there are four months where Melbourne’s monthly record is lower than Auckland’s all-time record. 

Melbourne is colder than Auckland in the sense that the minimum temperature (in a typical period of a few years) is lower, and the minimum is an important summary statistic for garden design.