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This is a two part article to describe rms
Part 1:
Find the sum and average of these numbers:
1,2,3,4,5
Answer:
sum= 15
Average: 15/5 = 3
That was easy ... they added up to 15 and there were five values.
So to get an average we:
1: Find the sum of the numbers (15 here)
2: Divide by how many digits are present (5 here).
An easy way of saying "the sum of" is ∑
So we could have said:
Find ∑ v where v = 1,2,3,4,5
Answer: ∑ v = 15 ie: The sum of the set of v digits =15
Then: (∑ v )/n = 3 ie: The sum of v digits divided by how many digits we have there. .... 15/5
We can choose any letter to sum. I chose v here, but any will do.
I chose n to represent the number of digits used (5 digits here), but any letter will do .... just declare what your letters represent until it becomes obvious.
Your turn:
Find ∑ y y = 2,1,4,3,5
Then find the mean
Answer:
Same as before .... it often helps to put numbers in order at the start.
The word "average" can be used for different things ... here the average is called the "mean".
The "mean" is a well used word for this method of finding an average.
One more go:
What is ∑ p² when p= 1,2,3,4,5
Then, what is the mean of those squared numbers? ie: what is (∑ p²)/n
Answer:
1+4+9+16+25
so the sum = 55 ie: ∑ p² = 55
"the sum of the p squareds is 55"
n=5 .... we have five digits.
So .... (∑ p²)/n = 55/5
ie: (∑ p²)/n = 11 that is our "mean" average for the squared values.
Sum = 55
Mean= 11
The "Mean" is a mathematical way of finding a centre point for a set of values.
Look at those value again from this example: 1+4+9+16+25 11 is right in the centre, even though not seen.
Now see RMS part 2 here:
http://everycircuit.com/circuit/5316067424731136
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