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Average, normal or median temperature?

There's really no such thing as a 'normal' high

Maybe it’s the cold weather, or just that I’m getting a little tired of winter, but a couple of my weather-related pet peeves have raised their ugly heads once again and I feel it’s my responsibility to address them. No, it’s not the argument about wind chill, I already tried to tackle that topic; this pet peeve has to do with the term “normal” temperature.

For those of you who have read my columns over the years you might have figured out that I really don’t like the idea of using average temperatures, or to be more specific, the term “normal” temperature. We almost never have average temperatures, so why do we use this as a gauge as to how warm or cold a particular day is? Then add the term “normal” and all of a sudden the general public seems to think that if we don’t see an average or “normal” temperature on any given day then that day is unusual.

If you look up what the term average means you will find several definitions, such as “a number expressing the central or typical value in a set of data” and “a single number taken as a representative of a list of numbers often referred to as the mean, which is the sum of all the numbers in a set divided by how many numbers make up the set.”

In statistics, the term mean is usually used instead of the term average. Along with the mean, there is also a median and mode. The median is the middle value of a set of numbers when they are ranked in order. The mode is the most frequently occurring number in a set of numbers. From a weather or climate point of view, mode isn’t that useful of a number, since many datasets will not have data points that repeat; therefore, there will often not be a mode.

The next question is: Which is better, the mean or the median? When there is a large dataset or if you have extreme outliers, then the median is often the better measure. The median will give a better representation of the central point of the dataset as it doesn’t get skewed by outliers — values that are at the extreme ends of the dataset. When I looked at mean and median values for daily high temperatures in Winnipeg over a 70-year period I found there was a small but significant difference between mean daily temperatures and median daily temperatures (see graph 1 at top). You might notice that both the daily mean and daily median vary from day to day, but when you look at daily averages or “normals” they tend to follow a smooth trend. This is because the data is usually smoothed or normalized to eliminate these daily temperature bumps, but this isn’t where my pet peeve lies. To me, using the mean to determine the central point for temperatures works, and normalizing the data isn’t that big of a deal. What I don’t agree with is using the term “normal,” along with all of the incorrect interpretation that goes along with it.

The term normal means a couple of things. Like the example above, it can be used to describe a dataset that has been adjusted or smoothed to make the data easier to see and understand. Normal is also a term used to describe the distribution of data around the mean. If the data follows a bell curve, where most data points occur around the mean and then the number of data points slowly drops off as you move away from the mean, then the data is said to be normally distributed. Looking at a couple of days of data and plotting the distribution around the mean, I found daily temperature data rarely, if ever, was normally distributed around the mean (see graph 2 below). So, while daily mean temperatures are normalized (smoothed), they are not usually normally distributed around the mean.

Using the term “normal” temperature tends to imply to the public that this is the temperature that we should experience on that given date. In reality, we rarely see the mean or “normal” temperature on any given date. I plotted out all the daily high temperatures for each day in January for Winnipeg from 1938 to 2008, just to see what it would look like. Graph 3 (below) shows all the data points along with the mean or average temperature (solid line). You can see that for most days there is a nearly equal number of days with above-average temperatures as below-average temperatures. Days with average temperatures rarely occur; it is either warmer or colder than average.

Therefore, I believe using a temperature range that indicates where most of the recorded temperature values for any given day have fallen is a better way to go. I use 95 per cent as my value when I create the temperature range in my forecasts. That means that 95 per cent of the temperatures that have been recorded on that date or period fall within the given temperature range. So, if a value occurs that is outside of this range, then it truly is a colder or warmer day than what would usually be expected.

Next week, my second weather pet peeve: “But it’s a ‘dry cold.’”

About the author

Co-operator contributor

Daniel Bezte is a teacher by profession with a BA (Hon.) in geography, specializing in climatology, from the U of W. He operates a computerized weather station near Birds Hill Park.


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