Intro to Business Statistics

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Variance

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Intro to Business Statistics

Definition

Variance measures the spread of data points in a dataset relative to the mean. It is calculated as the average of the squared differences from the mean.

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5 Must Know Facts For Your Next Test

  1. Variance quantifies how much individual data points differ from the mean.
  2. The formula for variance in a population is $$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$$, where \(x_i\) represents each data point, \(\mu\) is the population mean, and \(N\) is the number of data points.
  3. For a sample, variance is calculated using $$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$$, where \(x_i\) represents each data point, \(\bar{x}\) is the sample mean, and \(n\) is the sample size.
  4. Variance can never be negative because it involves squaring each difference from the mean.
  5. A higher variance indicates greater spread in the data points around the mean.

Review Questions

  • What does variance measure in a dataset?
  • How do you calculate variance for a population?
  • Why can variance never be negative?

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