Answer: Simplification by subtracting assumed mean and dividing by class width (h).
- A Direct formula applying raw class marks without taking any shortcut
- B Simplification by subtracting assumed mean and dividing by class width (h)
- C Decomposition of the frequency expression into separate partial fractions
- D Taking the logarithm of each class mark before averaging the result
Correct answer: B. Simplification by subtracting assumed mean and dividing by class width (h)
Explanation: Step-deviation: ui = (xi - a)/h where a is assumed mean and h is class width. Mean = a + (sum(fiui)/sum(fi)) × h.
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