‘Average’ conditions? They are anything but
Typical rainfall and sunshine means one thing to meteorologists and another to readers
“AVERAGE” IS one of the most sloppily used words in weather reports in the news media.
I, too, have to plead guilty to being less than rigorous in my own use of the word.
One of the difficulties is that the correct use of statistical terms might keep a mathematician happy but it would leave most other readers cold. It can also get very repetitive.
Apart from its general meaning of “typical”, average is also a synonym for the arithmetic mean. Often shortened to “mean”, this is what you get when you add up a set of measurements and divide by the number of measurements. For instance, to discover the mean maximum temperature for December 2011, one adds together each daily maximum during the month and divides by 31.
Another word which can be misleading is “normal”. Too-clever-by-half correspondents upbraid me for writing loosely about “normal rainfall” and “normal sunshine”, suggesting – usually with a touch too much sarcasm – that I might like to write a column about abnormal sunshine.
There are, though, secondary meanings: in the scientific study of climate, “normal” refers specifically to the mean value over a 30year period of any meteorological element at a particular site.
The arithmetic mean provides a good summary of a set of measurements when they cluster evenly around a particular value. Unfortunately, not all meteorological elements do this. The distribution may be skewed – with a cluster towards one extremity and stragglers towards the other, or there may be more than one cluster, and so on. When this happens statisticians may look at the median and the mode as well as the mean. The median is defined as that value which has half of the measurements above it and half below; the mode is the value which occurs most frequently in the set of measurements.
Let us look at an example. The number of days with a snow-cover in the Januaries of the 1960s in Bedfordshire were, respectively, 3, 0, 9, 31, 2, 3, 10, 0, 13, and 0. For this strongly skewed set of observations the mean is 7.1, the median is 3, and the mode is 0. Each of these figures shows up a different characteristic of the set, and taken together they tell us a great deal more than does the mean itself.