Variance vs Standard Error

Variance quantifies spread by averaging squared deviations from the mean, so it is always non-negative. The sample variance is $s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2$, where $x_i$ are the values, $\bar{x}$ (x-bar) is the mean, and $n$ is the number of values. For example, data tightly packed around the mean have a small variance. Because the deviations are squared, variance is measured in squared units, and its square root is the standard deviation.

The standard error plays the same role for a statistic that the standard deviation plays for raw data, and it gets smaller as the sample size grows. For example, the standard error of a sample proportion is $\sqrt{\frac{p(1-p)}{n}}$ (the square root of p times one minus p, divided by n). For a sample mean it is $\frac{\sigma}{\sqrt{n}}$ (sigma, the population standard deviation, over the square root of n). A smaller standard error means the estimate is more precise, which narrows a confidence interval.