Question

The following data are from a simple random sample: 1, 4, 7
The point estimate of the population standard deviation is:

• A. 2
• B. 5
• C. 1.5
• D. 3

Answer 1

The Correct Option is D

To calculate the point estimate of the population standard deviation, we begin with finding the sample standard deviation of the given data: 1, 4, 7. First, we calculate the mean (\( \bar{x} \)) of the sample:

\(\bar{x}=\frac{1+4+7}{3}=4\)

Next, determine the squared differences from the mean:

(1 - 4)\(^2\) = 9

(4 - 4)\(^2\) = 0

(7 - 4)\(^2\) = 9

The variance (s\(^2\)) of the sample is the average of these squared differences:

\(s^2=\frac{9+0+9}{3-1}=9\)

Now, find the sample standard deviation (s) as the square root of the variance:

\(s=\sqrt{9}=3\)

Thus, the point estimate of the population standard deviation is 3.