title: Calculating Population Standard Deviation in R
body: <p>Looking for a way to calculate Population Standard Deviation in R -- using greater than 10 samples. Unable to extract the source C code in R to find the method of calculation.</p>
  
  <pre><code># Sample Standard Deviation 
  # Note: All the below match with 10 or less samples
  n &lt;- 10 # 10 or greater it shifts calculation
  set.seed(1)
  x &lt;- rnorm(n, 10)
  
  # Sample Standard Deviation
  sd(x)
  # [1] 0.780586
  sqrt(sum((x - mean(x))^2)/(n - 1))
  # [1] 0.780586
  sqrt(sum(x^2 - 2*mean(x)*x + mean(x)^2)/(n - 1)) # # Would like the Population Standard Deviation equivalent using this.
  # [1] 0.780586
  sqrt( (n/(n-1)) * ( ( (sum(x^2)/(n)) ) - (sum(x)/n) ^2 ) )
  # [1] 0.780586
  </code></pre>
  
  <p>Now, the Population Standard Deviation needs to match sd(x) with 100 count.</p>
  
  <pre><code># Population Standard Deviation 
  n &lt;- 100 
  set.seed(1)
  x &lt;- rnorm(x, 10)
  
  sd(x)
  # [1] 0.780586
  
  sqrt(sum((x - mean(x))^2)/(n))
  # [1] 0.2341758
  
  sqrt(sum(x^2 - 2*mean(x)*x + mean(x)^2)/(n)) 
  # [1] 0.2341758
  
  # Got this to work above using (eventual goal, to fix the below):
  # https://en.wikipedia.org/wiki/Algebraic_formula_for_the_variance
  sqrt( (n/(n-1)) * ( ( (sum(x^2)/(n)) ) - (sum(x)/n) ^2 ) )  # Would like the Population Standard Deviation equivalent using this.
  # [1] 3.064027
  </code></pre>