The following data was collected from a simple random sample of a population. 13 15 14 16 12
The point estimate of the population standard deviation is
A)2.500
B)1.581
C)2.000
D)1.414

Question

Quizplus · Accepted Answer

To estimate the population standard deviation, we use the formula s = sqrt(Σ(xi-x̄)²/(n-1)) where x̄ is the mean of the sample, xi is each data point, and n is the sample size.

Plugging in the values from the sample, we get:

s = sqrt(((13-14.0)² + (15-14.0)² + (14-14.0)² + (16-14.0)² + (12-14.0)²) / 4)
s = sqrt((1² + 1² + 0² + 2² + (-2)²)/4)
s = sqrt(10/4)
s = sqrt(2.5)

Therefore, the point estimate of the population standard deviation is s = 1.581.

Option B is the answer.

The Following Data Was Collected from a Simple Random Sample