Which of the statements below are TRUE regarding the mean and standard deviation?
I As the number of measurements increases,approaches $\mu$ if there is no random error.
II The square of the standard deviation is the average deviation.
III The mean is the center of the Gaussian distribution.
IV The standard deviation measures the width of the Gaussian distribution.
A)II,III,and IV
B)I,III,and IV
C)I and II
D)I,II,and IV
E)III and IV

Question

Quizplus · Accepted Answer

III and IV are true. The mean is indeed the center of the Gaussian (normal) distribution, and the standard deviation measures the width of this distribution, indicating how spread out the values are from the mean. Statement I is incorrect because as the number of measurements increases, the mean approaches the true mean (μ) of the population, not necessarily 0, regardless of random error. Statement II is incorrect because the square of the standard deviation is the variance, not the average deviation.

Which of the Statements Below Are TRUE Regarding the Mean μ\muμ

Which of the Statements Below Are TRUE Regarding the Mean $\mu$