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Variance of Sample Mean

HardA/B Testing & Experimentation00:00
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Your question is Variance of Sample Mean. Take a moment with it on the right.

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Problem

Prove the variance of the sample mean / explain why the standard deviation of the sample mean is sigma/sqrt(n).

Asked in the ML depth/breadth stage. Explain the assumptions required for the result, including independence and identical variance. Connect the derivation to experiment sample-size planning without introducing a business scenario.

  1. Derive the variance and standard error step by step.
  2. State how the result changes with correlated observations or unequal variances.
  3. Show how the formula informs an MDE-based two-arm experiment.