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I'm and just somewhat confused about this topic.

Lets say I have a sample set A with sample size= 101 mean =10 and sample stdv of 1

then sample set B with sample size= 100 Mean=15 with sample stdv of 2.

If i add these two samples sets together I should get a new stdv that is no smaller than the smallest stdv of the two. Right?

If you don't agree please tell so I know Im wrong but if you do think that it is true, then here is my confusion.

Fourier Series and make a straight line say(y=1) a sum of different sine/cosine waves.

Now if I take the x values as the sample names and the y axis values as the test values of that sample. I can calculate a sample stdv for each wave. If i add the whole Fourier series together and get a straight line I would get a Stdv of zero. Which is less thant whatever the individual cosine/sine waves stdv were.

Thank you =)

I took one engineering stats course.