Standard Error is the standard deviation of samples drawn from the same population. Standard Error can be calculated for any statistical term like the standard error of the **mean**, **median,** or **proportion**.

- Standard Error helps in finding the difference between population statistics and sample statistics.
- Standard Error indicates how well sample data represent the population.

Standard Deviationindicates the spread of data.

#### Standard Error Formula

**1. When Population Standard Deviation is Known**

Standard Error =

where

- = standard deviation of the population.
**n**= sample size

**2. When Population Standard Deviation is Unknown**

Standard Error =

where

**s**= standard deviation of the sample.**n**= sample size

#### High Standard Error

- It indicates that the sample is not a good representation of the population.
- High uncertainty in population data due to which every sample drawn from that population has different statistics (like mean, median).

#### Low Standard Error

- It indicates that the sample data is a good representation of the population.
- Having a low standard error is good as it indicates the sample mean is very close to the population mean.

#### Standard Deviation vs Standard Error

- The
**standard deviation**represents variability**in the sample**. - The
**standard error**estimates the variability**across multiple samples**from the same population.