Statistics
Mean and variance with missing observations
MMTS_Full_Test_04
Grade 12
Question:
The mean and variance of 7 observations are 8 and 16 respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the remaining two observations are
(A) 5, 7
(B) 6, 8
(C) 8, 9
(D) 7, 8
Step-by-Step Solution
Key Concept: Set up two equations: sum of all 7 = mean×7, and sum of squares of all 7 = $n(\sigma^2+\bar{x}^2)$.
$x+y=14$, $x^2+y^2=100$. Solve: $(x,y)=(6,8)$.
Correct Answer: (B) 6, 8