Math Help - Empirical Moments problem

1. Empirical Moments problem

Hello again, I hope I'm not getting on peoples nerves yet with my constant question. :/

I have the following problem:

Given the table:
x 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
f 1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1
(doesn't quite look like I table, I know)

a.) Calculate x (with a line on top, referring to m-prime-sub-1, the first moment about the origin)

b.) Calculate s

I'm annoyed that I can't get this myself. I have the formula right in front of me, but I just can't seem to apply it correctly.

$m'_{{k}} \left( x \right) ={\frac {\sum _{i=1}^{k}{x_{{i}}}^{k}f_{{i}}}{n}}$

I was able to get the answer to a.) in Maple using
X := <(seq(i, i = 1 .. 12))> :
F := <(1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1)> :
Moment(X, 1, weights = F)
(= 4.43)

Is there a function to get the sample (s)? Either way it'd be nice to know how both formulas are applied without Maple.

Any help (again) would be appreciated.

 Also, if I have multiple questions on different (but related, Statistics) questions, is it customary or helpful for others that I post those in separate threads?

2. Originally Posted by BklynKid
Hello again, I hope I'm not getting on peoples nerves yet with my constant question. :/

I have the following problem:

Given the table:
x 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
f 1, 7, 11, 16, 8, 4, 5, 2, 1, 0, 0, 1
(doesn't quite look like I table, I know)

a.) Calculate x (with a line on top, referring to m-prime-sub-1, the first moment about the origin)

b.) Calculate s
$n=\sum f_i = 56$

$\bar{x}=\frac{1}{n}\sum f_i ~x_i$

and by s I presume you mean the 2-nd central moment:

$s=\frac{1}{n}\sum (x_i-\bar{x})^2 f_i$

RonL

3. Thanks again for the help.