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If the standard deviation of the numbers −1, 0, 1, k is √5 where k > 0, then k is equal to:
- 2√6
- 2√(10/3)
- 4√(5/3)
- √6
Correct answer: 2√6
Solution
The standard deviation is calculated based on the variance, which involves the mean of the numbers. By setting up the equation for variance using the given numbers and solving for k, we find that k must equal 2√6 to satisfy the condition that the standard deviation equals √5.
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