# 4. Standard Error of the Sample Mean

## f. calculate and interpret the standard error of the sample mean;

What is a standard error and why is it important?

The standard error of a statistic is the standard deviation of the sampling distribution of that statistic. Standard errors are important because they reflect how much sampling fluctuation a statistic will show.

What happens to the standard error of a statistic when given a larger or smaller sample size?

- In general the larger a sample size the smaller the standard error.

- The size of the standard error of the mean is inversely proportional to the square root of the sample size (see the math notation for standard error of the mean)

What is the math symbol for "standard error of the sample mean"?

$$\sigma_m$$

What is the standard error of the mean and what is the math formula for it?

- Standard error of the mean is the standard deviation of the sampling distribution of the mean.

- $$\sigma_m = \frac{\sigma}{\sqrt{N}}$$

What is the standard error of the mean (`\sigma_m`

) for a sampling distribution of: standard deviation (`\sigma`

) = 100, sample size (`N`

) = 10, sample mean (`\bar{m}`

) = 530

- $$\sigma_m = \frac{\sigma}{\sqrt{N}}$$

- `\sigma_m = 100 / 10^{1/2} = 31.62`

##### Source:

- CFA