Answer: It gives more weight to extreme values and has algebraic tractability.
- A It is easier to calculate since it largely avoids using absolute values
- B It gives more weight to extreme values and has algebraic tractability
- C It tends to be smaller in value than the mean deviation in practice
- D It equals the variance directly, making the two values interchangeable
Correct answer: B. It gives more weight to extreme values and has algebraic tractability
Explanation: SD squares deviations (more sensitive to outliers), is algebraically tractable, and has favorable mathematical properties for further analysis.
In a perfectly normal (bell-shaped) distribution, mean, median, and mode all coincide at the centre; about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 - the empirical rule used to judge how typical or extreme a value is.
Concept context
Mean, median, mode, standard deviation, and data interpretation