Sum of Squares help!

JWade

New Member
#1
My homework problem says:

For the following summary statistics, find ∑X and SS (sum of squares)

a. XBar = 25, s = 10, n = 11

So, I think that ∑X = 225 but am having trouble how to find SS. Thanks in advance for any help!
 

spunky

Super Moderator
#4
My homework problem says:

For the following summary statistics, find ∑X and SS (sum of squares)

a. XBar = 25, s = 10, n = 11

So, I think that ∑X = 225 but am having trouble how to find SS. Thanks in advance for any help!
In my notes I have that XBar = ∑X/N .. so I did 25 = ∑X/11 .. 25 x 11 = 225

Is that not right?
your thought process is right but the algebra is where the issue is. try it again in a calculator, how much is 25 x 11?

for the second question here's a small hint. you have the standard deviation. from the standard deviation you can get the variance, right? and if you had real data and not the standard deviation, how is it that you calculate the variance? what would the formula be?
 

JWade

New Member
#5
Oops, I have 275 written down, not sure why I typed 225.

So, standard deviation = s, which is 10... so to get the variance you just square it, right?

The formula I have is s^2 = ∑(X - XBar)^2 / n-1
 

Dragan

Super Moderator
#6
Well, it will turn out that you have one equation with one unknown when you expand the numerator of the expression (the summation operator expands through the parentheses after the expansion) as you have provided above - given the real constants you have provided.
 

spunky

Super Moderator
#8
just substitute the values that you already have in the formula for the variance that you wrote in your previous post.

you're so cloooose!!! :D
 

JWade

New Member
#9
I am getting so confused because, if I just plug in my values, what am I solving for? In my mind, (which I'm sure is incorrect which is why it isn't making sense...)it's looking like this:

10^2 = (275 - 25)^2 / 10 ... What am I doing wrong? Clearly there's not a variable to solve for. I just don't understand what I am supposed to be doing I guess... the only thing I have written in my notes for SS is Sum of Squares/Degrees of Freedom ... and I can't find much help online as to what SS even is. I feel stumped.
 

spunky

Super Moderator
#10
all i'm going to say at this point is that the formula for the variance and the formula for the sum of squares are somehow related. and they are related in a non-tricky, you-should-be-able-to-notice-it kind of way.

you can definitely take it from there.
 

Dason

Ambassador to the humans
#12
You've already written that you know this:

s^2 = ∑(X - XBar)^2 / (n-1)

Can you identify which part of that is the sum of squares?
 
#13
No, I can't. I don't understand sum of squares. I just started this class, have never had statistics in my life, and I'm trying to understand but I am just getting vague answers and telling me I should just "get it" ... Well, I don't. I have been trying to figure it out for 2 days now.
 
#15
Yes I have a professor, the homework is due Wednesday, which is when I next have class, and I was really having trouble with this problem and stumbled on this website. Made an account hoping to get some help with it. Now I just feel like an idiot since the problem is apparently so simple and I just am missing something. If all of you understand I don't get why you can't help me. Oh well.
 

Dragan

Super Moderator
#16
Well, take a deep breath - you have the Summation(X) correct: 275=(n)*(XBar), Mkay.

That said, the Variance for your variable X is equal to: Variance(X) = SS(X)/(n-1), where (n-1) is your degrees of freedom. You are given the standard deviation for your variable X i.e., s=10. So what is the relationship between the variance of X and the standard deviation of X? Once you have that, you can solve for the SS(X).

I hope this helps.
 
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#18
YMade an account hoping to get some help with it. Now I just feel like an idiot since the problem is apparently so simple and I just am missing something. If all of you understand I don't get why you can't help me. Oh well.
Forum rules [agreed to, when creating each account] disallow solving homework problems by giving whole answers. An easy answer might be unethical and sometimes problematic, as it interferes with the process of learning and even might be considered cheating.
Otherwise, it would be much easier for most of forum contributors to simply write the complete solution and leave to the next thread, instead of patiently trying to highlight the problem through asking questions and giving hints.

On another note, it is pretty natural to put 2 days on a statistics/math problem. I for one have put months on some of my problems to no avail! :)
 
#19
Well, take a deep breath - you have the Summation(X) correct: 275=(n)*(XBar), Mkay.

That said, the Variance for your variable X is equal to: Variance(X) = SS(X)/(n-1), where (n-1) is your degrees of freedom. You are given the standard deviation for your variable X i.e., s=10. So what is the relationship between the variance of X and the standard deviation of X? Once you have that, you can solve for the SS(X).

I hope this helps.
So, the standard deviation is the square root of the variance. So, that would mean if the standard deviation is 10, the variance is 100?

So.. x=1000...?
 

Dragan

Super Moderator
#20
Well, yes, basically you're correct. In more detail, it would be the Sums of Squares associated with the variable X, which is 1000. Note, that this is what I perceived from the very beginning, which is based on your query in your original post, JWade.