Asked by Fakaapo. Suetusi
Whether multiplying the same number to each value in the data set will affect its variance, please can you gave me an example.
Thank you for your help.
Thank you for your help.
Answers
Answered by
MathMate
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?
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?