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For a sample of 10 measurements, the squared deviations from the mean sum to 45. What is the sample standard deviation, to two decimals?
A4.50
B2.12
C2.24
D5.00
Answer & Solution
Correct answer: C. 2.24
1. For a sample, the variance divides the summed squared deviations by n - 1, not n.
2. Compute the sample variance: 45/(10 - 1) = 45/9 = 5.
3. The standard deviation is the square root of the variance: sqrt(5).
4. sqrt(5) is approximately 2.24.
5. Option B, 2.12, is sqrt(45/10), the population-style divisor applied to sample data.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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