Answer:
The Standard Deviation is a measure of how spread out numbers are. You might like to read this simpler page on Standard Deviation first. But here we explain the formulas. The symbol for Standard Deviation is σ (the Greek letter sigma)
1/6 of the shingles/ 2 stacks= 1/12 of the shingles/stack.
There will be 1/12 of the shingles in each stack~
![\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ %The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3} \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad \begin{cases} 8829=3\cdot 3\cdot 3\cdot 327\\ \qquad 3^3\cdot 327 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%25The%20volume%20of%20two%20spheres%20are%20327%5Cpi%20in%5E%7B3%7D%20and%208829%5Cpi%20in%5E%7B3%7D%0A%5Ccfrac%7Bsmall%7D%7Blarge%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7B327%7D%7D%7B%5Csqrt%5B3%5D%7B8829%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0A8829%3D3%5Ccdot%203%5Ccdot%203%5Ccdot%20327%5C%5C%0A%5Cqquad%203%5E3%5Ccdot%20327%0A%5Cend%7Bcases%7D)
![\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7B327%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E3%5Ccdot%20327%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Cunderline%7B%5Csqrt%5B3%5D%7B327%7D%7D%7D%7B3%5Cunderline%7B%5Csqrt%5B3%5D%7B327%7D%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B1%7D%7B3%7D)