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Test: Variance and standard deviation

This test develops calculation and interpretation of the mean, variance and standard deviation. Tasks compare data spread, examine the effect of outliers and assess whether a sample reliably represents a population.

Question qty: 10
Duration in minutes: 18
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Sample questions

  • How do sample size and sampling method affect reliability?
  • Standard deviation is s. Every value is multiplied by k. What is the new standard deviation?
  • What does a standard deviation of 0 mean?
  • Calculate the population variance of: d.
  • Sets A and B have equal means. Their standard deviations are a and b. Which set is more spread out?
  • The variance is v. Find the standard deviation.
  • The variance is v. The value c is added to every observation. What is the new variance?
  • Find the mean of: d.

Variance and standard deviation

Variance is the mean of the squared deviations of data values from their mean. Standard deviation is the square root of variance, so it has the same units as the original data.

Interpreting spread

Find the mean, each deviation, its square and the mean of those squares. A small standard deviation indicates values clustered closer to the mean. Compare both centre and spread, and check whether the required formula is for a complete population or a sample.

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