Subtopic: Mean, median, mode and standard deviation
Question Statement:
Which of the following statements is/are TRUE regarding statistical measures of central tendency and dispersion?
Options:
(A) The arithmetic mean is sensitive to extreme values (outliers)
(B) The median is robust against extreme outliers
(C) The standard deviation is independent of change of origin
(D) The coefficient of variation is defined as $\frac{\sigma}{\mu} \times 100$
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
1. The mean uses all values, so extreme outliers heavily shift it (A is true).
2. The median depends only on rank order, so extreme outliers do not alter the center rank (B is true).
3. Adding a constant $c$ to all observations shifts the mean by $c$ but leaves distances from the mean and standard deviation unchanged: $\sigma(X + c) = \sigma(X)$ (C is true).
4. The coefficient of variation is the relative standard deviation expressed as percentage: $CV = \frac{\sigma}{\mu} \times 100$ (D is true).