Statistics
Finding missing observations from mean and variance
nta_pyq_2023_jan
Grade 11
Question:
The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is
Step-by-Step Solution
Key Concept: From mean: $a + b = 16$. From variance: $a^2 + b^2 = 130$. Solve for $a$ and $b$, then compute $a^3 + b^3$.
$a + b = 16$, $a^2 + b^2 = 130 \Rightarrow a = 7$, $b = 9$. $a^3 + b^3 = 343 + 729 = 1072$.
Correct Answer: 1