estimation of mean and variance Why are so many efforts spent on estimation and comparison of mean, but not variance?  
For example, t-tests are used to comparing the population mean. 
When reporting the data, we usually describe the data as mean and its standard error. Why are not reporting the estimated variance and its uncertainty? 
 A: Whether we are interested in estimation of the mean, or variance, or both, or neither, depends on context.  Statistics has well developed methods for estimating and comparing means or variances, though the former is more commonly used in introductory statistical courses, and is more widely known.  There are certain contexts where mean differences are of most interest (e.g., in surveys and controlled experiments) and there are other contexts where variance and covariance are of most interest (e.g., in some financial models).  It is not unusual for students to encounter methods for estimating and comparing means when they first learn statistics.
Having said this, it is worth noting that, as a broad rule, lower order moments of a distribution tend to be more "fundamental" than higher-order moments, and when we aggregate applications of statistical methods over all contexts, it tends to be the case that people are mostly interested in location (mean), then scale (variance), then skewness, kurtosis, etc.  This tendency occurs because most distributions can be reasonably well approximated by looking at their low-order moments.  Just as we can approximate a broad class of functions by appropriate finite-degree polynomials (Taylor approximation), we can similarly approximate a broad class of distributions by finite-degree moment approximations (e.g., via methods like Edgeworth expansion, etc.).
