Q269 / 270 · NDA 2022 (Phase 1) · Mathematics

$\begin{array}{|c|c|c|c|c|c|}\hline Class & 0-20 & 20-40 & 40-60 & 60-80 & 80-100 \\\hline Frequency & 17 & p+q & 32 & p-3 q & 19 \\\hline\end{array} The total frequency is 120 . The mean is 50 . What is the value of $q$ ?

  • Correct answer
    A
    1
  • B
    2
  • C
    3
  • D
    4

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} $68+2 P-2 q \quad 3480+100 p-180 q$ $\therefore 68+2 P-2 q=120$ $\Rightarrow \mathrm{p}-\mathrm{q}=26$...(i) $\begin{aligned} & 50=\frac{3480+100 P-180 q}{120} \\ & 6000=3480+100 P-180 q\end{aligned}$ $\Rightarrow 5 P-9 q=126$...(ii) On solving equation (i) and (ii) we get $\mathrm{P}=27$ and $\mathrm{q}=1$

Hence, the correct answer is option: 'A'.

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