Posted by Fakaapo. Suetusi on Wednesday, April 18, 2012 at 4:42am.
Suppose the dataset is:
x(i)=1,3,5,7,9
sum=∑x=25
mean=μ=25/5=5
x(i)^2=1,9,25,49,81
sum of squares=∑x^2=165
Var(x)=(165-5^2)/5=28
If all the numbers in the dataset are multiplied by 2:
x(i)=2,6,10,14,18
sum=∑x=50
mean=μ=50/5=10
x(i)^2=4,36,100,196,324
sum of squares=∑x^2=660
Var(x)=(660-10^2)/5=112 (=4*28)
What can you say about the effect on variance of multiplying the dataset by a constant?