Statistics Questions

Let's say i had a group of numbers and now i know the mean, median, mode, and range for this group how do i calculate the variance?

Now let's say i want to statistically create a new list based off of the information from the first list.
How would i go about doing that?

Basically what i'm looking for is a way to create a new list with the size of the new list to be specified by the user and once created it will have the same statistical distribution with some randomness and variance built into it.

Easy examples would be nice! :>)
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aikimarkConnect With a Mentor Commented:
You asked me how you could calculate the variance.  What do you mean "How do I use it?"

I would try to create your new list similar to the following:
For I=0 to Ubound(itemarray) -2 Step 2
   itemarray(I) = avg + rnd() * (StandardDeviation/N)
   itemarray(I+1) = avg - rnd() * (StandardDeviation/N)

Where StandardDeviation/N is the square root of the variance divided by the number of items in the list.

Note: this assumes that you have an even number of items in your array.  Otherwise, you will have to create a random number = (rnd() * (StandardDeviation/N) * 2) -(StandardDeviation/N)
to be added to each item in the array.
Anthony PerkinsCommented:
Please maintain this open question:
FTP Append Method Date: 07/02/2001 09:13AM PST

the variance is the sum of the squares of the (item-avg) differences.
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jrcpAuthor Commented:
Okay, so how do you use the variance?
you can calculate the mean and variance of a list fairly easily, i could come up with code for that.

Making the new list depends on the distribution type you are interested in.
jrcpAuthor Commented:
I would be interested in a normal distribution... If i had some code or info on that I could modify it to change the distribution if i needed to. Just a little rusty on the stats.
jrcpAuthor Commented:
Just to check....

So if my list was

The variance would be
1 + 4 + 9 + 16 + 25 + 36 = 91/6 = 15.1

I guess this seems high since each number is only 1 apart, or it's just because i don't know how you use the variance.
If your list were:
The average = (1+2+3+4+5+6)/6 = 21/6 = 3.5

The variance would be
(3.5-1)^2 + (3.5-2)^2 + (3.5-3)^2 + (3.5-4)^2 + (3.5-5)^2 + (3.5-6)^2 = 2.5^2 + 1.5^2 + .5^2 + -.5^2 + -1.5^2 + -2.5^2 = 17.5
jrcpAuthor Commented:
What i meant by "how do i use it" is what is the purpose of variance?  I thought that variance would come into play when trying to create a new list with the same properties. It looks like i'm confused on the difference between std dev and variance.
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