We want to know the mean income of the population but the statistics provided to us are divided into four groups, North, South, East, and West. We do not know the sample size for the four groups, only the estimated group populations, incomes, and standard errors.

If possible, how do we estimate the mean and standard error for the total population?

.Group    .Count    .Income  .Standard Error
North     10,000    100      10
South     20,000    80       10
East      20,000    150      12
West      10,000    120      15
TOTAL     60,000    ??       ??

Thanks.

[May be related to http://stats.stackexchange.com/questions/135445/confidence-interval-for-sum-of-means which has an answer with a "-2"]