"\\sigma=\\sqrt{\\sigma^2}"
"\\mu_1={1\\over n}\\displaystyle\\sum_{i=1}^nx_{i1}=62"
"\\sigma_1^2={1\\over n}\\displaystyle\\sum_{i=1}^n(x_{i1}-\\mu_1)^2=8^2"
Given that
"x_{i2}=x_{i1}+5,\\ i=1,2,...,n"Then
"\\sigma_2^2={1\\over n}\\displaystyle\\sum_{i=1}^n(x_{i2}-\\mu_2)^2=""={1\\over n}\\displaystyle\\sum_{i=1}^n((x_{i1}+5)-(\\mu_1+5))^2=""={1\\over n}\\displaystyle\\sum_{i=1}^n(x_{i1}-\\mu_1)^2=\\sigma_1^2=8^2"
The mean will increase by 5 (it will be "67").
The standard deviation will remain the same (it will be "8").
Comments
Leave a comment