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WEATHER JOURNAL: Why The Average Isn’t Always “Normal”

almanac

Hi everyone, Brett here!

Spring has been very reluctant to lock in across the state this year, with a top-3 coldest March of the last 3 years, and now a very up-and-down April that has seen highs in the 70s in Des Moines, as well as the 40s — on back-to-back days no less!

In the meantime, it seems every time we show the daily almanac are temperatures are nowhere near “normal.” Or are they?

We commonly refer to the “Average High Temperature” as “normal,” but really is that accurate? It depends on the definition, but a lot of statisticians will say no. An average is just that. A single number. A more accurate way to define normal requires you to specify a range of temperatures.

For example: In March, we saw 19 days that were 10 or more degrees off of the average high! 19! We had 9 days 15 degrees off of the average! But did you know, that really isn’t unusual?

Did you know that, in fact, one might be able to say that in March we could typically expected to have 13 or 14 such extreme days?

Check this out. Say a particular day has an average high temperature over 5 years of 10 degrees. Say the temperature each of the 5 days was 9, 9, 10, 11, and 11. All pretty similar. How widely the numbers vary, called the “standard deviation” would be small.

But let’s consider something else. Here is another day with the same average of 10 over five years. -15, 4, 10, 16, and 35. See how it varies quite a bit? Even though it averages 10, the odds of picking one of those numbers and being close to ten isn’t very good, especially compared to the first group. This example is like our March high temperatures.

We’re used to wild swings in March. And since we have cold, snowy months in March (like this year) and 80 degree streaks in March (like last year) it is a wildly varying set of temperatures making up that average.

So back to that gross statistic, “standard deviation”. In March, most days are hovering somewhere around 12.8 for a standard deviation. Lets use March 15 as an example.

On March 15, the average high temperature is 49 with a standard deviation of 13 degrees. All this means, is there is a pretty good chance (about 68%) the high temperature will be 13 degrees, high or low, of 49. That means anywhere from 36 to 62 is “normal,” statistically speaking of course.

The chart below shows the actual number of occurrences of a certain temperature on March 15 (dashed line). The solid dark lines are the cumulative distribution (odds the temp gets at least to that temp).

march15

In fact, based on just random chance you could expect a roughly one-in-three chance that the daily high would fall OUTSIDE of that range! That’s TWICE-A-WEEK.

And those 19 days that were 10 or more off of the average. Well in March, it would seem there is roughly a 44% that any given day will be that extreme! Almost a 50/50 chance, which is not that out of the ordinary.

So keep that in mind the next time I slip up and call the average “normal.”

And in case you’re curious….the variance/standard deviation does change throughout the year. By July and August, it shrinks to 6 or 7 degrees depending on the day. So on those days of an average high at 86, statistically “normal” highs would fall in the 80-92 range.

A 10 degree extreme off the average on a random day in July? Somewhere around a 13% chance.

A 15 degree extreme day? We had nine of those in March. In July, it’s somewhere between a 2% and 3% chance! Makes all those 100+ degree days last year at 15 or 20 degrees higher than average seem all the more unlikely!

july15

You can play around an check out some of the statewide averages and deviations for any day you want here, at the Iowa Environmental Mesonet. And even if this lecture just put you to sleep, give the link a click anyway and help me thank them for providing the data for your sleeping aid!

–Brett



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