# Thread: "Combined" Means and Variances?

1. ## "Combined" Means and Variances?

Hi everyone.

This is my first stat assignment of the semester and I am already confused. I'm not sure what my prof is asking. I will reproduce the assignment below so that it makes sense when I ask my questions:

"
Country % Welfare Spending %65 and over
US 36.6 11.9
GE 48.9 14.8
FR 40.8 12.9
IT 32.8 12.9
UK 21.7 15.1
CA 35 10.4
AU 45.5 14.3
VBE 43.7 13.8
DE 43.5 15.1
FI 26.8 12.5
GR 26.9 13.4
IC 13.1 10.1
LU 46.7 13.2
NE 36.4 12.1
NO 31.5 15.7
PO 29 12
SP 51.6 12
SW 44.2 17.2
SZ 48.1 13.9
AL 24.5 10.2
NZ 24.1 10.2

1) What is the mean of "%welfare" and "%65 and over"? What does this statistic tell us?

2) What is the variance of "%welfare" and "%65 and over"? What does this statistic tell us?

3) What is the covariance between "%welfare" and "%65 and over"? What does this statistic tell us?"

Ok, now in question one (1), is he asking for two different "means" (i.e. the mean of all the values for %Welfare Spening and a separate mean for all the values of %65 and over)? Or is there some way to get some single, grand, combined mean of the values in both columns?

My confusion on question two (2) is similar, except with respect to variance.

Could someone perhaps clarify what my professor is unwilling to?

2. ## Re: "Combined" Means and Variances?

I guess the question is asking you to compute the sample mean and variances
for each column separately. You should be able to find out the formula

However, if you are really interested in estimating the overall mean and
variance, one simple way to estimate it is just pool them together.
If you have extra information about the two variables, you can also add
different weight to them.

3. ## Re: "Combined" Means and Variances?

1) Give the mean of %welfare column
and Give the mean of %65 and over column

2) Give the variance of %welfare column
and Give the mean of %65 and over column

3) Give the covariance between <%welfare and %65 and over>

4. ## Re: "Combined" Means and Variances?

Thank you to both contributors.

I'll tackle the problems tomorrow and then report back to you guys if I have any problems.

Thank you once more.

5. ## Re: "Combined" Means and Variances?

Ok, I'm back.

Now, in response to the three questions that my assignment asked for (which were in my original post), I have the following answers for the data given:

1) Mean of “%welfare” = 35.78
Mean of “%65 and over” = 13.03

2) Variance of “%welfare” = 105.57
Variance of “%65 and over” = 3.59

3) Covariance of “%welfare” and “%65 and over” = 9.12

Now what I still am not quite understanding is, with the exception of covariance, what each of these measures tell us.

For example, what does the "mean" of each of those variables tell us? I know that it is an "average" but what does that really mean?

Secondly, what does the variance tell us in general and what do these specific variance values mean in this case?

Thirdly, even though I know that a positive value for covariance means that higher than average values of one variable tend to be paired with higher than average values of another, what is noteworthy specifically of the fact that the covariance in this case is 9.12 as opposed to being, say, 1.0?

If anyone is willing and able to shed light on the above, I would appreciate it.

6. ## Re: "Combined" Means and Variances?

Originally Posted by stud40111
Ok, I'm back.

For example, what does the "mean" of each of those variables tell us? I know that it is an "average" but what does that really mean?

Secondly, what does the variance tell us in general..
Your questions are rather complicated. I would think of your questions in terms of Physics.

Specifically, the mean is the first moment and is an index that finds the center of gravity of a data set.

Further, think of variance as (a function) of the second moment, which can be considered as an index of the inertia (or spread) of a data set.

7. ## Re: "Combined" Means and Variances?

Originally Posted by Dragan
Your questions are rather complicated. I would think of your questions in terms of Physics.

Specifically, the mean is the first moment and is an index that finds the center of gravity of a data set.

Further, think of variance as (a function) of the second moment, which can be considered as an index of the inertia (or spread) of a data set.
I see what you are saying when you say that my questions are rather complicated. However, I think that perhaps my professor is not looking for that in depth of an answer given that this is only the first week of our class. Is there perhaps a simpler way to sum up what the mean, variance and COVARIANCE tell us about the data?

Regardless, thank you for your help.

8. ## Re: "Combined" Means and Variances?

What does 65% mean?
I mean what is the context of this question?

9. ## Re: "Combined" Means and Variances?

What does 65% mean?
I mean what is the context of this question?
"%65 and over" means "Percentage of the Population 65 and over".

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