Central Tendency & DispersionPYQ June 23Question 3227 of 473
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If the first quartile is 42.75\displaystyle 42.75 and the third quartile is 74.25\displaystyle 74.25, then the coefficient of QD is:

Options

A29.62\displaystyle 29.62
B15.75\displaystyle 15.75
C17.57\displaystyle 17.57
D26.92\displaystyle 26.92
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Correct Answer

✅ Option d — 26.92\displaystyle 26.92

All Options:

  • A29.62\displaystyle 29.62
  • B15.75\displaystyle 15.75
  • C17.57\displaystyle 17.57
  • D26.92\displaystyle 26.92

Detailed Solution & Explanation

We are given: - First quartile: Q1=42.75\displaystyle Q_1 = 42.75 - Third quartile: Q3=74.25\displaystyle Q_3 = 74.25 The coefficient of quartile deviation is calculated as: Coefficient of Q.D.=Q3−Q1Q3+Q1×100\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100 Coefficient of Q.D.=74.25−42.7574.25+42.75×100=31.5117×100≈26.92%\text{Coefficient of Q.D.} = \frac{74.25 - 42.75}{74.25 + 42.75} \times 100 = \frac{31.5}{117} \times 100 \approx 26.92\% Hence, **Option D** is the correct answer.

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