Answer:
[tex]\mathrm{Decimal:\quad }\:38.8[/tex]
Step-by-step explanation:
[tex]\frac{\left(3-11\right)^2+\left(5-11\right)^2+\left(13-11\right)^2+\left(14-11\right)^2+\left(20-11\right)^2}{5}\\\left(3-11\right)^2+\left(5-11\right)^2+\left(13-11\right)^2+\left(14-11\right)^2+\left(20-11\right)^2=194\\\left(3-11\right)^2+\left(5-11\right)^2+\left(13-11\right)^2+\left(14-11\right)^2+\left(20-11\right)^2\\\left(3-11\right)^2=64\\\left(3-11\right)^2\\\mathrm{Subtract\:the\:numbers:}\:3-11=-8\\=\left(-8\right)^2[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad\left(a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}\\\left(-8\right)^2=8^2\\8^2=64\\\left(5-11\right)^2=36\\\left(5-11\right)^2\\\mathrm{Subtract\:the\:numbers:}\:5-11=-6\\=\left(-6\right)^2\\\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}\\\left(-6\right)^2=6^2\\=6^2\\6^2=36\\\left(13-11\right)^2=4\\\left(13-11\right)^2\\\mathrm{Subtract\:the\:numbers:}\:13-11=2\\=2^2\\2^2=4\\\left(14-11\right)^2=9[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:14-11=3\\=3^2\\3^2=9\\\left(20-11\right)^2=81\\\left(20-11\right)^2\\\mathrm{Subtract\:the\:numbers:}\:20-11=9\\=9^2\\9^2=8\\=64+36+4+9+81\\\mathrm{Add\:the\:numbers:}\:64+36+4+9+81=194\\=194\\=\frac{194}{5}\\\mathrm{Decimal:\quad }\:38.8[/tex]
