માહિતી
વર્ગ 4-8 8-12 12-16 16-20
આવૃત્તિ 3 \(\lambda\) 4 7
નો મધ્યક અને વિચરણ અનુક્રમે જો \(\mu\) અને 19 હોય. તો \(\lambda+\mu\) નું મૂલ્ય ___ છે.

A 18
B 21
C 20
D 19

Verified Solution

Answer & Solution

Correct Answer

(D) 19

Step-by-step Solution

Detailed explanation

\(\mu=\frac{\sum f_i x_i}{\sum f_i}=\frac{18+10 \lambda+56+126}{14+\lambda}\) \(=\frac{200+10 \lambda}{\lambda+14}=10+\left(\frac{60}{\lambda+14}\right)\) \(\lambda+14\) is multiply of \(60 \Rightarrow \lambda=1\) or 6 or 16. \(\sigma^2=\frac{\sum x_1^2}{\lambda+14}-(\mu)^2\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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વર્ગ	4-8	8-12	12-16	16-20
આવૃત્તિ	3	\(\lambda\)	4	7

માહિતીવર્ગ4-88-1212-1616-20આવૃત્તિ3\(\lambda\)47નો મધ્યક અને વિચરણ અનુક્રમે જો \(\mu\) અને 19 હોય. તો \(\lambda+\mu\) નું મૂલ્ય ___ છે.

Step-by-step Solution

માહિતી
વર્ગ 4-8 8-12 12-16 16-20
આવૃત્તિ 3 \(\lambda\) 4 7
નો મધ્યક અને વિચરણ અનુક્રમે જો \(\mu\) અને 19 હોય. તો \(\lambda+\mu\) નું મૂલ્ય ___ છે.