Statistics
Mean and Variance of Frequency Distribution
nta_pyq_2023_apr
Grade 11
Question:
For the frequency distribution $x_i: 2,4,6,8,10,12,14,16$ and $f_i: 4,4,\alpha,15,8,\beta,4,5$ with mean 9 and variance 15.08, then $\alpha^2+\beta^2-\alpha\beta$ is _____.
Step-by-Step Solution
Key Concept: Use $\bar{x}=9$ to get $\alpha=\beta$. Then use variance $=15.08$ to solve for $\alpha$.
$\alpha=\beta=5$. $25$.
Correct Answer: 25