The estimated population standard deviation of the scores 2, 4, 6 is.
A)0.67
B)1.00
C)2.00
D)4.00

Question

Quizplus · Accepted Answer

The standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. For the data set 2, 4, 6, the mean is 4. The squared deviations from the mean are (2-4)^2 = 4, (4-4)^2 = 0, and (6-4)^2 = 4. The average of these squared deviations is (4+0+4)/3 = 8/3. The square root of 8/3 is approximately 1.63, which is not an option here. However, the mistake in the question seems to be in the interpretation of "estimated population standard deviation." Normally, for a population standard deviation, we would divide by N (the number of data points), but for a sample, we divide by N-1 to get an unbiased estimate. Using N-1 (in this case, 2), the calculation should be sqrt((4+0+4)/2) = sqrt(4) = 2, which matches option C. This suggests a misunderstanding in the question's wording, as it directly asks for the population standard deviation but the correct calculation aligns with a sample standard deviation approach.

The Estimated Population Standard Deviation of the Scores 2, 4