SOLUTION: find the standard deviation first 13 natural numbers?

Question 1018958: find the standard deviation first 13 natural numbers?
Answer by Marz157(7) (Show Source): You can put this solution on YOUR website!
I'm going to assume that your definition of Natural numbers starts a 1, so the first 13 are the numbers from 1 to 13.
Also I'm assuming that you are getting the population standard deviation which means we will use N instead of N-1 later on.
So for standard deviation we will first need the mean (also called the average). For that we need to sum all the numbers and divide by how many numbers we added up (in this case 13).
There is a nice trick for summing up numbers starting at 1 which is
which gives us 91 for n=13. When we divide by n to get the average, we get 7.
Standard deviation is defined as the square root of the sum of the squared errors divided by n (or sometimes n-1, check with your teacher for what they want).
The "error" means the difference from the mean. So for example the error for the first number 1 is (7-1 = 6). We square this to get 36.
We do this for each number and add them up.
1) 7-1 = 6, 6*2 = 36
2) 7-2 = 5, 5^2 = 25
3) ... 16
4) ... 9
5) ... 4
6) ... 1
7) ... 0
8) ... 1
9) ... 4
10) ... 9
11) ... 16
12) ... 25
13) ... 36
Summing those we get 182. We divide 182 by 13 since we have 13 numbers = 14. Lastly we take the square root to get 3.7416
Wikipedia has a great example of computing a standard deviation https://en.wikipedia.org/wiki/Standard_deviation#Basic_examples
RELATED QUESTIONS
find the mean and the standard deviation of the first n natural... (answered by Fombitz)

find the sum of the first 328 even natural... (answered by Alan3354,solver91311)

find the sum of first n natural... (answered by longjonsilver)

Find the mean of first n natural... (answered by stanbon)

Find the aremides mean of first n natural numbers (answered by stanbon)

How do I : Find the sum of the first 400 natural... (answered by jim_thompson5910,scott8148)

Find 1+2+3+4+...+140, the sum of the first 140 natural... (answered by ikleyn,Alan3354)

Find the smallest number that is divisible by first 10 natural numbers. (answered by solver91311)

Find the sum of 300 natural... (answered by Alan3354)