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The standard deviation of the observations x1, x2,..., xn is 2. If the sum of the observations is 20 and the sum of their squares is 100, then the value of n is
- 10 or 20
- 5 or 10
- 5 or 20
- 5 or 15
Correct answer: 5 or 20
Solution
SD=2 so variance=4. Then 100/n - (20/n)^2 = 4 -> 100n - 400 = 4n^2 -> n^2 - 25n + 100 = 0 -> n = 5 or 20. Answer: 5 or 20.
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