Question Number 20705 by mondodotto@gmail.com last updated on 01/Sep/17
Answered by dioph last updated on 01/Sep/17
![40 = ((Σx_i −(43+35)+(34+53))/(200)) 8000 = Σx_i − 78 + 87 Σx_i = 7991 m = ((Σx_i )/(200)) = ((7991)/(200)) m = 39.955 15 = (√(([Σx_i ^2 −(43^2 +35^2 )+(34^2 +53^2 )]−[(Σx_i −(43+35)+(34+43))^2 /200])/(199))) 225 = (([Σx_i ^2 + 891]−[8000^2 /200])/(199)) 44775 = Σx_i ^2 − 319109 Σx_i ^2 = 363884 σ = (√((Σx_i ^2 −(Σx_i )^2 /200)/(199))) σ = (√((363884−7991^2 /200)/(199))) σ ≈ 14.971](https://www.tinkutara.com/question/Q20708.png)
$$\mathrm{40}\:=\:\frac{\Sigma{x}_{{i}} −\left(\mathrm{43}+\mathrm{35}\right)+\left(\mathrm{34}+\mathrm{53}\right)}{\mathrm{200}} \\ $$$$\mathrm{8000}\:=\:\Sigma{x}_{{i}} \:−\:\mathrm{78}\:+\:\mathrm{87} \\ $$$$\Sigma{x}_{{i}} \:=\:\mathrm{7991} \\ $$$${m}\:=\:\frac{\Sigma{x}_{{i}} }{\mathrm{200}}\:=\:\frac{\mathrm{7991}}{\mathrm{200}} \\ $$$${m}\:=\:\mathrm{39}.\mathrm{955} \\ $$$$\mathrm{15}\:=\:\sqrt{\frac{\left[\Sigma{x}_{{i}} ^{\mathrm{2}} −\left(\mathrm{43}^{\mathrm{2}} +\mathrm{35}^{\mathrm{2}} \right)+\left(\mathrm{34}^{\mathrm{2}} +\mathrm{53}^{\mathrm{2}} \right)\right]−\left[\left(\Sigma{x}_{{i}} −\left(\mathrm{43}+\mathrm{35}\right)+\left(\mathrm{34}+\mathrm{43}\right)\right)^{\mathrm{2}} /\mathrm{200}\right]}{\mathrm{199}}} \\ $$$$\mathrm{225}\:=\:\frac{\left[\Sigma{x}_{{i}} ^{\mathrm{2}} \:+\:\mathrm{891}\right]−\left[\mathrm{8000}^{\mathrm{2}} /\mathrm{200}\right]}{\mathrm{199}} \\ $$$$\mathrm{44775}\:=\:\Sigma{x}_{{i}} ^{\mathrm{2}} \:−\:\mathrm{319109} \\ $$$$\Sigma{x}_{{i}} ^{\mathrm{2}} \:=\:\mathrm{363884} \\ $$$$\sigma\:=\:\sqrt{\frac{\Sigma{x}_{{i}} ^{\mathrm{2}} −\left(\Sigma{x}_{{i}} \right)^{\mathrm{2}} /\mathrm{200}}{\mathrm{199}}} \\ $$$$\sigma\:=\:\sqrt{\frac{\mathrm{363884}−\mathrm{7991}^{\mathrm{2}} /\mathrm{200}}{\mathrm{199}}} \\ $$$$\sigma\:\approx\:\mathrm{14}.\mathrm{971} \\ $$