[tex]x_1=a\\x_2=a+10\\x_3=a+20\\x_4=a+30\\x_5=a+40\\\\n=5\\\\X=\frac{x_1+x_2+x_3+x_4+x_5}5=\frac{a+a+10+a+20+a+30+a+40}5=\frac{5a+100}5=\frac{5(a+20)}5=a+20[/tex]
[tex]\sigma^2=\frac{(x_1-X)^2+(x_2-X)^2+...+(x_n-X)^2}{n}\\\\\sigma^2=\frac{(a-(a+20))^2+(a+10-(a+20))^2+(a+20-(a+20))^2+(a+30-(a+20))^2+(a+40-(a+20))^2}5\\\\\sigma^2=\frac{(a-a-20)^2+(a+10-a-20)^2+(a+20-a-20)^2+(a+30-a-20)^2+(a+40-a-20)^2}5\\\\\sigma^2=\frac{(-20)^2+(-10)^2+0^2+10^2+20^2}5\\\\\sigma^2=\frac{400+100+0+100+400}5\\\\\sigma^2=\frac{1000}5=200\\\\\sigma=\sqrt{200}=\sqrt{2*100}=10\sqrt2[/tex]
