Working with correlation coefficients I have three Pearson correlation coefficients (.8978, .5676 and .7865) for three age groups (i.e. 21 to 30 years, 31 to 40 years and 41 to 50 years) whose behavior I am studying in regard to their shopping habits versus weight gain.
Can I say that .8978 is the strongest relationship between shopping habits and weight gain? 
Based on the difference in the coefficients, can I say that there is a difference in the shopping habits and weight gain of the three age groups?
Finally, can I just add the the three coefficients and divide by three to come up with an average?
All these are 'face value' interpretations. Are they acceptable or do I need to perform  some sort of statistical analysis? If it is the latter (heaven forbid), can SPSS do it? 
 A: Averaging correlation coefficients is a meaningless operation. Correlation is $$\rho = \frac{\mbox{Cov}[X,Y]}{\sqrt{\mbox{Var}[X]\mbox{Var}[Y]}}.$$ You cannot even average the components of it (the covariance and two variances), unless the means of all groups on both variables are the same. If they are not, your population variance/covariance will be larger than/different from the (weighted) sum of variances/covariances due to between-group differences.
A: 
Can I say .8978 is the strongest relationship between shopping habits and weight gain?

Descriptively, you can say that it is the strongest relationship. Whether it is significantly stronger than the other two depends on your sample size. There's an online calculator for that.

Based on the diffference in the coefficients, can I say that there is a difference in the shopping habits and weight gain of the three age groups?

That's the same statistical question as above. Test each pair of correlations for the significance of the difference. As you perform three tests, you might want to think about a correction of the $\alpha$ level.
Another possibility elaborated here would be to add age group as a dummy coded variable into a regression analysis.

Finally, can I just add the the three coefficients and divide by three to come up with an average?

No. To get an average correlation you have to do an $r$-to-$Z$ transformation (Fisher's $Z$), average these transformed values, and backtransform the average $Z$ to an $r$ again. For the transformation, there are several online calculators. 
