Central Tendency & DispersionPYQ June 24Question 3230 of 473
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If in a data set, 25\displaystyle 25 percent of values are smaller than 30\displaystyle 30 and one-fourth of values are larger than 70\displaystyle 70, then the coefficient of quartile deviation is _________ %

Options

A40\displaystyle 40
B30\displaystyle 30
C70\displaystyle 70
D50\displaystyle 50
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Correct Answer

✅ Option a — 40\displaystyle 40

All Options:

  • A40\displaystyle 40
  • B30\displaystyle 30
  • C70\displaystyle 70
  • D50\displaystyle 50

Detailed Solution & Explanation

We are given: - 25%\displaystyle 25\% of values are smaller than 30  ⟹  \displaystyle 30 \implies the first quartile (Q1\displaystyle Q_1) is 30\displaystyle 30. - One-fourth (25%\displaystyle 25\%) of values are larger than 70  ⟹  \displaystyle 70 \implies the remaining 75%\displaystyle 75\% are smaller than 70\displaystyle 70, which means the third quartile (Q3\displaystyle Q_3) is 70\displaystyle 70. Calculate the coefficient of quartile deviation: 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.=70−3070+30×100=40100×100=40%\text{Coefficient of Q.D.} = \frac{70 - 30}{70 + 30} \times 100 = \frac{40}{100} \times 100 = 40\% Hence, **Option A** is the correct answer.

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