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For a sample of 20 ages the frequency weighted squared deviations total 9.7375. What is the sample standard deviation to two decimal places?
AIt is s = 0.72
BIt is s = 0.49
CIt is s = 0.70
DIt is s = 0.51
Answer & Solution
Correct answer: A. It is s = 0.72
1. The sample variance divides the total squared deviation by the sample size minus one.
2. The sample size is 20 students, so the divisor is 19.
3. Dividing 9.7375 by 19 gives a variance of 0.5125 years squared.
4. The standard deviation is the square root of that, which is 0.7159 years.
5. Rounded to two places the sample standard deviation is 0.72 years.
6. Reporting 0.51 leaves the answer as the variance, and 0.70 comes from dividing by 20 instead of 19.
_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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