In

statistics, standard error is the

standard deviation of a

distribution of sample

means. The formula for it is -

s.e = σ
---
√n

Why is this useful?

Imagine we want to know the pH of water in a river. It is not feasible to measure the pH of every single drop of water, hence we would tend to measure the pH of a sample of water and calculate the result from this. You might estimate the mean of the pH by finding the mean of a sample.

Our confidence in how accurate measuring the sample mean and using it as an estimator of the population mean depends on the variance of the sample means we pull out. Imagine we take ten samples and they give us sample means between 3 and 7. Obviously, we're not very confident of the accuracy of our samples in this case! If they gave us sample means in a narrower range, such as between 7 and 8, we might be more confident.

Standard errors are used in calculating confidence intervals for data.