Standard deviation

Definition

Standard deviation is a measure of the dispersion or spread of a set of data points around its mean. It quantifies how much the individual data points deviate from the mean value.

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. A low standard deviation indicates that data points are close to the mean, while a high standard deviation indicates that they are spread out over a wider range of values.
4. In hypothesis testing, standard deviation is crucial for determining confidence intervals and conducting z-tests or t-tests.
5. The empirical rule states that for a normal distribution, approximately 68% of data points lie within one standard deviation from the mean, 95% within two, and 99.7% within three.

Review Questions

• What does it mean if a dataset has a high standard deviation?
• How do you interpret the empirical rule in relation to standard deviation?
• What symbol represents sample standard deviation and how is it different from population standard deviation?

Related terms

Variance: A measure of how much values in a dataset differ from the mean; it is the square of the standard deviation.

Confidence Interval: A range of values derived from sample statistics that is likely to contain the true population parameter with a specified level of confidence.

Student's t-Distribution: A probability distribution used in hypothesis testing for small sample sizes or when the population variance is unknown.