# Pooled sample mean formula?

1. Nov 23, 2013

### joe342

We have variable X (Active companies with a credit score)
and variable Y (Bankrupt companies with a credit score)

The mean, variance, n etc for their credit scores are known for X and Y. (We are given a lot of information about these companies, but a lot of this information is irrelevant hence the "etc")

I am asked to find the mean and variance for both the bankrupt and active companies creditscores put together without adding the creditscores together.

I found the variance by using the pooled sample variance formula.
My problem is finding the mean. Is there such a thing as a pooled sample mean?

2. Nov 23, 2013

### haruspex

If the mean of a dataset is m and there are n numbers in the dataset, what is the total of the numbers?

3. Nov 23, 2013

### joe342

hmmm ... then n is sum of X divided by mean?

4. Nov 23, 2013

### haruspex

Yes, but in this case you know the mean of each of two datasets and the number of data items in each, so you can reconstruct the total for each. Then you can calculate the mean of the combined dataset.

5. Nov 23, 2013

### anonymousk

Aah .. so:
((sum of x)*(sum of Y)) / ((mean of X)*(mean of Y))?

(I have a similar assignment, but seems I did it wrong)

6. Nov 23, 2013

### haruspex

Umm.. what do you think that would calculate?

7. Nov 23, 2013

### joe342

Do i divide sum of X with mean of x, then divide sum of Y with mean of Y. Then what? Just add the sums together?

8. Nov 24, 2013

### haruspex

We don't seem to be on the same wavelength.
As I understand it, there are two datasets, X and Y. You know the mean of each and the number of data items in each. You are not told the sum of each.
In order to get the overall mean, you need (sum of all of X and Y combined)/(number items in X and Y combined), yes?
If that's all correct, how will you find (sum of all of X and Y combined) and (number items in X and Y combined)?

9. Nov 24, 2013

### anonymousk

Well, in my case I have:

Mean, variance and n for the credit scores of active businesses (X)
and mean, variance and n for the credit scores of bankrupt business (Y)

I have to calculate the mean and variance for them put together (without adding them on top of each other. Says we can't assume they are normally distributed if they are added together.

So for the variance I used the pooled variance formula, but not sure how I'll go about calculating the mean

10. Nov 24, 2013

### haruspex

Finding the mean of an aggregate of two sets of numbers has nothing to do with probability or distributions. It's really simple.