Question

数据中每个数都乘2,标准差怎么变

Answer 1

标准差也乘以2

证明:

S1=根号{[(X1-X平)^2+(X2-X平)^2+(X3-X平)^2+……+(Xn-X平)^2]/n}

每个数乘以2后

S2=根号{[(2X1-2X平)^2+(2X2-2X平)^2+(2X3-2X平)^2+……+(2Xn-2X平)^2]/n}

=根号{4[(X1-X平)^2+(X2-X平)^2+(X3-X平)^2+……+(Xn-X平)^2]/n}

=2根号{[(X1-X平)^2+(X2-X平)^2+(X3-X平)^2+……+(Xn-X平)^2]/n}=2S1