Standard deviation

Definition

Standard deviation measures the dispersion of a dataset relative to its mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates data points are spread out.

5 Must Know Facts For Your Next Test

1. Standard deviation is denoted by $\sigma$ for a population and $s$ for a sample.
2. It is calculated as the square root of the variance.
3. In hypothesis testing, standard deviation helps determine the spread of sample means when constructing confidence intervals.
4. For small sample sizes where population standard deviation is unknown, the t-distribution is used instead of the normal distribution.
5. Standard deviation plays a crucial role in measuring risk and variability in business statistics.

Review Questions

• What does a high standard deviation signify about a dataset?
• How is standard deviation related to variance?
• Why do we use the t-distribution instead of the normal distribution when dealing with small sample sizes?

Related terms

Variance: Variance is the average of the squared differences from the mean and measures how far each number in the set is from the mean.

Confidence Interval: A confidence interval is a range of values derived from sample statistics that likely contains the value of an unknown population parameter.

Hypothesis Testing: Hypothesis testing involves making inferences about populations based on sample data, often using tests like z-tests or t-tests to determine statistical significance.