Statistics
Mean and Variance — Finding a+3b
DAILY_CHALLENGE
Grade 11
Question:
Let the mean and the variance of 6 observations $a,b,68,44,48,60$ be 55 and 194 respectively. If $a>b$, then $a+3b$ is
Step-by-Step Solution
Key Concept: Mean: $a+b+68+44+48+60=330\Rightarrow a+b=110$. Variance: $\frac{\sum(x_i-55)^2}{6}=194\Rightarrow(a-55)^2+(b-55)^2=800$. Solve with $a+b=110$.
$a=75,b=35$. $a+3b=180$.
Correct Answer: 3