Vega Tran
07/08/2024 · Elementary School

Question 4 Given the variance \( \sigma^{2} \) of 40 for a data set, what is the standard deviation \( \sigma \) ?

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The relationship between variance and standard deviation is given by the formula: \[ \sigma = \sqrt{\sigma^{2}} \] Given that the variance \( \sigma^{2} \) is 40, we can substitute this value into the formula to find the standard deviation \( \sigma \). \[ \sigma = \sqrt{40} \] Now, we can calculate the standard deviation. Calculate the value by following steps: - step0: Calculate: \(\sqrt{40}\) - step1: Write as a product: \(\sqrt{4\times 10}\) - step2: Write in exponential form: \(\sqrt{2^{2}\times 10}\) - step3: Use the properties of radicals: \(\sqrt{2^{2}}\times \sqrt{10}\) - step4: Simplify the root: \(2\sqrt{10}\) The standard deviation \( \sigma \) is approximately 6.324555.

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The standard deviation \( \sigma \) is approximately 6.324555.
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