Answer: σ/√n.
- A σ/n
- B σ × n
- C σ/√n
- D σ²/n
Correct answer: C. σ/√n
Explanation: For n iid observations each with variance σ², Var(X̄) = Var(ΣXᵢ/n) = nσ²/n² = σ²/n. So SEM = SD(X̄) = σ/√n. Doubling n halves the SEM, reflecting improved precision of the sample mean estimate.
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