Question

$$S_{j(n_{j})}^{2}=\frac{\sum(x_{i}-\overline{x}_{j(n)})^{2}}{n_{j}-1}$$

Answer

$$s=(Sj(n*j)^2+1)/(u*m*n*j*(x*IM-e^2*IM*o*v*r*l*n^2*x*j)^2)$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{Sj(nj)}^{2}=sum{(x\imath -ov{e}^{2}rl\imath {n}^{2}xj)}^{2}nj-1\]
Regroup terms.
\[{Sj(nj)}^{2}=sum{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}nj-1\]
Regroup terms.
\[{Sj(nj)}^{2}=sumnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}-1\]
Regroup terms.
\[{Sj(nj)}^{2}=-1+sumnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Add \(1\) to both sides.
\[{Sj(nj)}^{2}+1=sumnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Divide both sides by \(u\).
\[\frac{{Sj(nj)}^{2}+1}{u}=smnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Divide both sides by \(m\).
\[\frac{\frac{{Sj(nj)}^{2}+1}{u}}{m}=snj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Simplify  \(\frac{\frac{{Sj(nj)}^{2}+1}{u}}{m}\)  to  \(\frac{{Sj(nj)}^{2}+1}{um}\).
\[\frac{{Sj(nj)}^{2}+1}{um}=snj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Divide both sides by \(n\).
\[\frac{\frac{{Sj(nj)}^{2}+1}{um}}{n}=sj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Simplify  \(\frac{\frac{{Sj(nj)}^{2}+1}{um}}{n}\)  to  \(\frac{{Sj(nj)}^{2}+1}{umn}\).
\[\frac{{Sj(nj)}^{2}+1}{umn}=sj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Divide both sides by \(j\).
\[\frac{\frac{{Sj(nj)}^{2}+1}{umn}}{j}=s{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Simplify  \(\frac{\frac{{Sj(nj)}^{2}+1}{umn}}{j}\)  to  \(\frac{{Sj(nj)}^{2}+1}{umnj}\).
\[\frac{{Sj(nj)}^{2}+1}{umnj}=s{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\]
Divide both sides by \({(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}\).
\[\frac{\frac{{Sj(nj)}^{2}+1}{umnj}}{{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}}=s\]
Simplify  \(\frac{\frac{{Sj(nj)}^{2}+1}{umnj}}{{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}}\)  to  \(\frac{{Sj(nj)}^{2}+1}{umnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}}\).
\[\frac{{Sj(nj)}^{2}+1}{umnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}}=s\]
Switch sides.
\[s=\frac{{Sj(nj)}^{2}+1}{umnj{(x\imath -{e}^{2}\imath ovrl{n}^{2}xj)}^{2}}\]