Sample mean

Definition

The sample mean is the average of a set of observations from a sample. It is calculated by summing all the observations and dividing by the number of observations.

5 Must Know Facts For Your Next Test

1. The sample mean is denoted by $\overline{x}$.
2. The Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size increases, regardless of the population's distribution.
3. The formula for calculating the sample mean is $\overline{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$.
4. The standard error of the mean decreases as the sample size increases, which makes the sample mean a more accurate estimate of the population mean.
5. In hypothesis testing, the sample mean is often used to make inferences about the population mean.

Review Questions

• What symbol is typically used to denote the sample mean?
• Explain how the Central Limit Theorem applies to sample means.
• How does increasing the sample size affect the standard error of the mean?

Related terms

Population Mean:

The average of all observations in a population, denoted by $\mu$.

Standard Error:

A measure of how much sampling variability exists in a statistic, calculated as $\frac{\sigma}{\sqrt{n}}$ for means.

Central Limit Theorem:

A theorem stating that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed.