What is the differences between standard deviation and standard error and when do we use either of them?

Answer 1

Standard Deviation is a measure of the spread of its values. It is defined as the square root of the variance.

The formula is σ = Σ((x-μ)^2)/N
where σ = Standard Deviation, x = individual variables, N = number of variables, μ = mean of variables

For example, in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be written: {4, 8} ≈ 6±2. In this case 100% of the values in the population are at one standard deviation of the mean.

Standard Error of an estimated or measured value is the standard deviation of the error in that value. In general, the standard error of a value is the estimated standard deviation of the error in the process by which it was generated.

SE = σ/√(n)
where SE = Standard Error, n = Number of variables, σ = Standard Deviation of the variables

Standard error is found in case of hypothesis testing and comparing populations.