Statistics
Combined Statistics
MMTS_Full_Test_07
Grade 12
Question:
An online exam is attempted by 40 candidates, 15 are boys. Average marks of boys is 10 with variance 2. Variance of marks of 25 girls is also 2 and average marks of all 40 is 12.5. If $\mu$ is average marks of 25 girls and $\sigma^2$ is variance of marks of all 40 candidates, then $20\sigma^2-8\mu=$
Step-by-Step Solution
Key Concept: Use combined mean and variance formulas
$\bar{x}_{all}=12.5$: $15\cdot10+25\mu=40\cdot12.5\Rightarrow\mu=14$. Combined variance: $\sigma^2=2+\frac{15\cdot 25}{40^2}\cdot(10-14)^2=2+\frac{375\cdot 16}{1600}=2+\frac{15}{4}=\frac{23}{4}$. Actually recalc: $20\cdot\frac{23}{4}-8\cdot 14=115-112=3$.
Correct Answer: 3