How is the sample standard deviation derived from the sample variance?

Conditions

• The corrected sample variance $S^2$ has been calculated.
• The square root taken is the principal (non-negative) root.

Reasoning, step by step

1. Identify the calculated sample variance $S^2 = 36$.
2. Apply the definition of sample standard deviation: $S = \sqrt{S^2}$.
3. Calculate the square root: $S = \sqrt{36} = 6$.

Example

The screen displays "The sample standard deviation is S = √$36 = 6$".

Common misconceptions

• Reporting the variance (36) as the standard deviation.
• Taking the negative square root (-6), although standard deviation is defined as non-negative.

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Connected concepts

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• How is the corrected sample variance calculated for the six pulse-rate data points?
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• Why is the sample standard deviation useful for interpreting the data?