Q268 / 270 · NDA 2022 (Phase 2) · Mathematics

Consider the following grouped frequency distribution : $\begin{array}{|l|l|l|l|l|l|l|} \hline \text { Class } & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 \\ \hline \text { Frequency } & 1 & 2 & 4 & 6 & 4 & 3 \\ \hline \end{array}$ What is the median of the distribution?

  • A
    $34$
  • B
    $34.5$
  • Correct answer
    C
    $35$
  • D
    $35.5$

Solution

$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Class } & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 \\ \hline \text { fi } & 1 & 2 & 4 & 6 & 4 & 3 \\ \hline \text { C.F. } & 1 & 3 & 7 & 13 & 17 & 20 \\ \hline \end{array}$ $\begin{aligned} & \frac{N}{2}=\frac{20}{2}=10 \\ & \therefore \quad \text { Median class }=30-40 \\ & \therefore \quad \text { Median }=l+\frac{\frac{N}{2}-C}{f} \times h . \\ & \mathrm{Me}=30+\frac{10-7}{6} \times 10 \\ & =30+5=35\end{aligned}$

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

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