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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Step-by-step Solution
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.
Quick Answer
The standard deviation \( \sigma \) is approximately 6.324555.
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