If the mean and the variance of the data Class 4-8 8-12 12-16 16-20 --- --- --- --- --- Frequency 3 λ 4 7 are μ and 19 respectively, then the value of λ+μ is

Mathematics · Probability

JEE Main 2026 — 23 January, Evening Shift — Question 18

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

$\mu=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{18+10 \lambda+56+126}{14+\lambda}$

$\mu=\frac{200+10 \lambda}{\lambda+14}=10+\left(\frac{60}{\lambda+14}\right)$

$\lambda+14$ is multiply of $60 \Rightarrow \lambda=1$ or 6 or 16 .

$\sigma^{2}=\frac{\sum \mathrm{x}_{1}^{2}}{\lambda+14}-(\mu)^{2}$

$\sigma^{2}=\frac{6^{2}+10^{2}(\lambda)+14^{2}+(18)^{2}(7)}{\pi+14}-\mu^{2}$

for $\lambda=6, \mu=10+3=13$

$\lambda+\mu=19$

Answer key and solution verified before publishing.

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