Statistics
Grouped Data — Mean and Variance, λ+μ
nta_pyq_2026_jan
Grade 11
Question:
If the mean and the variance of the data (Class 4–8, 8–12, 12–16, 16–20; Frequency 3, $\lambda$, 4, 7) are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is
Step-by-Step Solution
Key Concept: Midpoints: 6, 10, 14, 18. $N=14+\lambda$. $\mu=\tfrac{200+10\lambda}{14+\lambda}$. $\sum f_ix_i^2=3(36)+100\lambda+4(196)+7(324)=3160+100\lambda$. Variance $=19$.
$\lambda=6$, $\mu=13$. $\lambda+\mu=19$.
Correct Answer: 2