Standard deviation and variance

• What is the standard deviation?

  The square root of the variance
• What does a small/ large standard deviation mea?

  • Small standard deviation: data is consistent
  • Large standard deviation: data is varied
• How does standard deviation relate to the normal distribution?

  It determines the spread of the results
• How is the range calculated?

  Highest score - Lowest score + 1
• What does variance measure in a data set?

  The spread of scores around the mean
• What does a small variance indicate?

  Scores are similar and close to the mean
• What does a large variance imply?

  Scores are different and far from the mean
• What are the steps to calculate variance?

  1. Calculate the mean (x or μ)
  2. Subtract the mean from each number (x - x)
  3. Square the results
  4. Sum the squared numbers (Σ)
  5. Divide by 'n' or 'n-1' for sample variance
• What is the formula for variance for a population?

  $\sigma^2 =$$\frac{\Sigma(X - \mu)^2}{N}$
• Strength of variance/ SD


  1. Take all scores into account. C: more precise and representative measurements
• Weakness of variance/ SD

  May hide some key characteristics in the data (E.g. Outliers). C: calculation is based on the mean which is not useful without a normal data distribution.