Paper 1 · descriptive statistics
A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is the variance of this distribution?
Model answer
11.7
Also accepted: 11.70
Explanation: E(X^2) = [2(1^2)+5(2^2)+7(4^2)+6(10^2)]/20 = [2+20+112+600]/20 = 734/20 = 36.7. Variance = E(X^2) - [E(X)]^2 = 36.7 - 5^2 = 36.7 - 25 = 11.7.
Derived from ZIMSEC Statistics Paper 1, November 2018, Q1
