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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Statistics

NDA 2022 · Mathematics · Statistics

Class 0-20 20-40 40-60 60-80 80-100 Frequency 17 p+q 32 p-3 q 19...

Class0-2020-4040-6060-8080-100
Frequency17p+q32p-3 q19
The total frequency is 120. The mean is 50. If the frequency of each class is doubled, then what would be the mean?

Options

  1. A25
  2. B50
  3. C75
  4. D100

Correct answer

B. 50

Step-by-step solution

\begin{array}{|c|c|c|c|}\hline C.I & \mathrm{f}_{\mathrm{i}} & \mathrm{x}_{\mathrm{i}}& \mathrm{f}_{\mathrm{i}} \mathrm{X}_{\mathrm{i}} \hline 0-20 & 17 & 10 & 170 \hline 20-40 & \mathrm{P}+\mathrm{q} & 30 & 30(\mathrm{P}+8) \hline 40-60 & 32 & 50 & 1600 \hline 60-80 & \mathrm{P}-3 \mathrm{q} & 70 & 70 \mathrm{P}-210 \mathrm{q} \hline 80-100 & 19 & 90 & 1710 \hline\end{array}68+2 P-2 q \quad 3480+100 p-180 q\therefore 68+2 P-2 q=120\Rightarrow p−q=\mathrm{p}-\mathrm{q}=26...(i)...(i)50=3480+100P−180q1206000=3480+100P−180q\begin{aligned}& 50=\frac{3480+100 P-180 q}{120}\\ & 6000=3480+100 P-180 q\end{aligned}⇒5P−9q=126...(ii)Onsolvingequation(i)\Rightarrow 5 P-9 q=126...(ii) On solving equation (i) and (ii) we get \mathrm{P}=27and27 and\mathrm{q}=1Iffrequencyof1If frequency ofeach class is doubled ∴ New Mean =∑i=1nxi2fi∑2fi=2∑i=1nxifi2∑fi=∑i=1nxifi∑fi=50\begin{aligned}& \therefore \text{ New Mean }=\frac{\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}} 2 \mathrm{fi}}{\sum 2 \mathrm{fi}}=2 \frac{\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}} \mathrm{fi}}{2 \sum \mathrm{fi}}\\ & =\frac{\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}} \mathrm{fi}}{\sum \mathrm{fi}}=50\end{aligned}
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