Intro to Statistics

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Standard deviation

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Intro to Statistics

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.

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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?

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