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I heard that yesterday the atmospheric pressure at my location was exceptionally higher than normal and that explained why I had such a terrible headache all day. But what remained unclear was...

How does atmospheric pressure vary in the same point on Earth?

Granted, it has to depend on location height above the sea level and temperature, but if these two variables stay the same, what else could make atmospheric pressure change?

And is the average atmospheric pressure throughout the planet always the same?

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