# What is the meaning of error in the standard error of the mean?

**standard error**is a statistical term that measures the accuracy with which a sample distribution represents a population by using

**standard deviation**. In statistics, a sample

**mean**deviates from the actual

**mean**of a population—this

**deviation**is the

**standard error of the mean**.

Subsequently, one may also ask, what does the standard error of the mean tell us?

The **Standard Error** ("Std Err" or "SE"), is an indication of the reliability of the **mean**. A small SE is an indication that the sample **mean** is a more accurate reflection of the actual population **mean**. A larger sample size will normally result in a smaller SE (while SD is not directly affected by sample size).

**Calculating Standard Error of the Mean**

- First, take the square of the difference between each data point and the sample mean, finding the sum of those values.
- Then, divide that sum by the sample size minus one, which is the variance.
- Finally, take the square root of the variance to get the SD.

Subsequently, one may also ask, how do you interpret standard error of measurement?

**Standard Error of Measurement is directly related to a test's reliability: The larger the SEm, the lower the test's reliability.**

- If test reliability = 0, the SEM will equal the standard deviation of the observed test scores.
- If test reliability = 1.00, the SEM is zero.

The standard **error of the mean**, also called the standard deviation of the **mean**, is a method used to estimate the standard deviation of a sampling distribution. To understand this, first we need to understand why a sampling distribution is required.