How do I obtain a pooled mean standard error?

Suppose we have each of K people (or groups) which we wish to pool each with variances, $V_text{k}$ and mean $m_text{k}$ based on a sample of size $n_text{k}$.

$$ Pooled Variance V = \frac{\Sum_text{k}(n_text{k}-1)V_text{k}}{\Sum_text{k}(n_text{k}-1)} $$

$$ Pooled Mean Standard Error = \Sqrt{V / \sum_text{k}n_text{k}}