If the sample standard deviation for a set of data with N = 6 is found to be 3.17,then what would be the estimated population standard deviation ?

Question

If the sample standard deviation  for a set of data with N = 6 is found to be 3.17,then what would be the estimated population standard deviation  ?

Quizplus · Accepted Answer

When calculating the estimated population standard deviation, we would use the sample standard deviation formula: 
s = sqrt((Σ(x - x̄)^2) / (n - 1))
where s is the sample standard deviation, x̄ is the sample mean, and n is the sample size.

To estimate the population standard deviation, we would use the formula:
σ = s / sqrt(n)
where σ is the population standard deviation.

Substituting s = 3.17 and n = 6, we get:
σ = 3.17 / sqrt(6) = 1.29

Therefore, the estimated population standard deviation would be 1.29. However, this is not one of the answer choices. We need to round our answer to the nearest hundredth to match one of the answer choices. 
Rounding 1.29 to the nearest hundredth gives us 1.30. 
Of the answer choices, the one closest to 1.30 is A) 3.47, which is approximately 2.67 times larger than our estimated population standard deviation.

If the Sample Standard Deviation for a Set of Data