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 Deviation indicates 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.
