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### Average Wind Direction

```
Date: 05/21/97 at 20:32:14
From: Josh Morcom
Subject: Average wind direction

We have a weather instrument that records wind direction once every
second. (A numerical value between 0 and 359)

Our problem is to calculate average wind direction once each hour
using 3600 samples.

Any help that you can give us will be greatly appreciated.

Josh Morcom
```

```
Date: 05/22/97 at 05:18:57
From: Doctor Mitteldorf
Subject: Re: Average wind direction

Dear Josh,

a clear answer!  Sometimes the idea of an "average wind direction"
makes sense, but sometimes it won't make any sense at all.

Here's an example of how it CAN make sense.  If the wind blows from
the east (90 deg) for half an hour and from the south (180 deg) for
half an hour, you can clearly say that the average wind direction for
that hour is southeast (180 + 90)/2 = 135 deg.

Here's an example of how it DOESN'T make sense. If the wind blows from
the east (90 deg) for half an hour and from the west (270 deg) for
half an hour, there really is no average direction at all. You could
say south, but you could just as well say north.

Here's what I would do if I were you. First look at the sample "by
eye" to see if the wind direction was pretty consistent, or if it
varied all over the map. If it varied too much, and had a lot of N, S,
E and W in it all in one hour, you just have to say that there is no
meaning to "average wind direction."

But if it's pretty consistent, then you can keep going. Let's say
that all the numbers are between 80 and 150 deg. Then you can just
add them all up and divide by 3600, the usual way you take an average.

It is a little trickier if the wind is coming approximately from the
north. Then there will be some numbers between 0 and 30, say, and
some more between 300 and 359. If that's the case, then you might add
360 to all the LOW numbers before you do the average. For every number
that's 0-30 you add 360, and for every number that's between 300 and
359 you keep the same.  Add them all up and divide by 3600 to get the

Here's one problem I'll leave you with: Suppose you do all that and
the answer you get is an average of 368 degrees.  What does that
really mean?

-Doctor Mitteldorf,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Statistics

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