Every number in a set is increased by 20%.
Palo Alto Networks technical mcq question, verified with a worked answer. Free to practise - no sign-up.
Every number in a set is increased by 20%. Analyse the following two statements and answer the question that follows:
Statement A: The median increases by 20%
Statement B: The mean increases by 20%
Then which of the following is true?
Select any one of the following options
Show answer & explanation
Multiplying every value in a dataset by a constant factor c = 1.20 scales both the arithmetic mean and the median by 1.20 (a 20% increase for both).
Step-by-step Derivation:
Step 1: Let values be x_1, x_2, ..., x_n. New values are y_i = 1.2 * x_i.
Step 2: Mean(Y) = (1/n) sum(1.2 * x_i) = 1.2 * Mean(X), so mean increases by 20% (Statement B is true).
Step 3: Median(Y) = 1.2 * Median(X) since relative order of sorted elements is preserved, so median increases by 20% (Statement A is true).
Step 4: Both statements are true.