MHB Standard Deviation: 10 & 11 Consecutive Positive Multiples of n

[greprep]

Hi, All. I'm trying to re-familiarize myself with standard deviations. Any resources? I'm reading through the threads here and trying to figure out the following:

"n is a positive integer.
What is the standard deviation of 10 consecutive positive multiples of n.
And what is the standard deviation of 11 consecutive positive multiples of n?"

Can the relationship not be determined from the information given? Many Thanks!

 

[MarkFL]

I would begin with the following formula for population standard deviation:

$$\sigma=\sqrt{\frac{\sum(x-\mu)^2}{N}}$$

Next, I would look at:

$$\mu=\frac{1}{N}\sum_{k=m}^{m+(N-1)}(kn)=\frac{n}{2}(2m+N-1)$$

And then:

$$\sum_{k=m}^{m+(N-1)}\left(kn-\frac{n}{2}(2m+N-1)\right)^2=\frac{n^2N\left(N^2-1\right)}{12}$$

And thus:

$$\sigma=\frac{n}{2}\sqrt{\frac{N^2-1}{3}}$$

Now you can use the above formula to answer the questions...:)