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?
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.
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