If the median (P) and mode (Q) satisfy the relation 7(Q-P)=9R, then what is the value of R?

Consider the following data for the next two (02) items that follow :<br><table> <thead><tr><th>Class</th><th>0–30</th><th>30–60</th><th>60–90</th><th>90–120</th></tr></thead> <tbody> <tr><td>Frequency</td><td>4</td><td>5</td><td>7</td><td>4</td></tr> </tbody> </table>

  1. A. 6
  2. B. 5
  3. C. 3
  4. D. 1

Correct Answer: A. 6

Explanation

Total frequency N=20. The median class is 60–90 (cumulative frequency crosses 10). Median P = 60 + \frac{10-9}{7} \times 30 = 60 + \frac{30}{7}. From the previous question, mode Q = 72. Substituting into 7(Q-P) = 9R, we get 7(72 - 60 - \frac{30}{7}) = 7(12) - 30 = 84 - 30 = 54 = 9R \implies R=6.

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