# Thread: Affects on Mean and Standard Variation

1. ## Affects on Mean and Standard Variation

I'll be honest: I missed the day this was gone over in class and I can't find it in my book. I understand the policy on homework questions so I will post the question and what I've done and hopefully someone can just help me understand it. I'm not asking for answers, just help.

"In each of the following, describe how the mean and the standard deviation of a data set are affected."
a) The number 10 is added to each value of the data set.
b) Each value of the data set is multiplied by 2.
c) each value of the data set is multiplied by -2.

I made a data set and calculated it's mean and standard deviation and then added 10 to each number in the data set and the mean increased by 10 while the standard deviation stayed the same. When I multiplied each number by 2 both the mean and the standard deviation changed. I'm not sure if the numbers are supposed to behave this way or if I'm doing something wrong. (I am NEVER missing a class again come hell or high water!!!)

Any help is greatly appreciated.

2. ## Re: Affects on Mean and Standard Variation

Hey Pinklily.

Hint - Do you know what E[X] and Var[X] are?

3. ## Re: Affects on Mean and Standard Variation

I looked into those and I don't think we've gone over them yet? However! My professor was willing to help me before class time. So, I was correct on the first part. The reason I was getting confused on the multiplication is because I got my data sets mixed up. Sleep deprivation and math don't mix very well lol. All the question was asking was how do the numbers behave under those circumstances, so add 10 and the mean changes by 10 but the standard deviation stays the same. Multiply by 2 and everything doubles etc.

4. ## Re: Affects on Mean and Standard Variation

You should look at what happens to E[2X], E[X+10], Var[2X] and Var[X+10] for more information to understand why it changes and how.

5. ## Re: Affects on Mean and Standard Variation

Originally Posted by Pinklily
"In each of the following, describe how the mean and the standard deviation of a data set are affected."
a) The number 10 is added to each value of the data set.
b) Each value of the data set is multiplied by 2.
c) each value of the data set is multiplied by -2.
What you missed from that class is a standard proposition: ${\bf{E}}(a\cdot{\bf{X}}+b)=a\cdot{\bf{E}}({\bf{X} })+b$
Where ${\bf{E}}$ is the expectation of that random variable ${\bf{X}}$

For a) $a=1~\&~b=10$

For b) $a=2~\&~b=0$

6. ## Re: Affects on Mean and Standard Variation

This is a P.S. & a scolding.
Here is the scolding: It was not until much later that I just happened to read the title of the post.
Please in any future always post the entire complete question is full detail.

Another standard proposition: ${\bf{\mathscr{V}}}(a\cdot{\bf{X}}+b)=a^2\cdot \bf {\mathscr{V}}({\bf{X}})$
Where $\bf {\mathscr{V}}$ is the variance of that random variable ${\bf{X}}$

For a) $a=1~\&~b=10$

For b) $a=2~\&~b=0$