If the first quartile in 56.50 and the third quartile is 77.50, then the co-efficient of QD is:

Option b: 15.67. Solution: We are given: - First quartile: Q1 = 56.50 - Third quartile: Q3 = 77.50 The coefficient of quartile deviation is calculated as: text{Coefficient of Q.D.} = Q3 - Q1/Q3 + Q1 x 100 text{Coefficient of Q.D.} = 77.50 - 56.50/77.50 + 56.50 x 100 = 21/134 x 100 approx 15.67% Hence, Option B is the correct answer.

Central Tendency & DispersionPYQ Dec 22Question 3223 of 473

All Questions

If the first quartile in $\displaystyle 56.50$ and the third quartile is $\displaystyle 77.50$ , then the co-efficient of QD is:

Options

\displaystyle 18.09

\displaystyle 15.67

\displaystyle 63.80

\displaystyle 156.71

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Correct Answer

✅ Option b — $\displaystyle 15.67$

All Options:

A $\displaystyle 18.09$
B $\displaystyle 15.67$
C $\displaystyle 63.80$
D $\displaystyle 156.71$

Detailed Solution & Explanation

We are given: - First quartile:

\displaystyle Q_1 = 56.50

- Third quartile:

\displaystyle Q_3 = 77.50

The coefficient of quartile deviation is calculated as:

\text{Coefficient of Q.D.} = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100

\text{Coefficient of Q.D.} = \frac{77.50 - 56.50}{77.50 + 56.50} \times 100 = \frac{21}{134} \times 100 \approx 15.67\%

Hence, **Option B** is the correct answer.

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If the first quartile in 56.50\displaystyle 56.5056.50 and the third quartile is 77.50\displaystyle 77.5077.50, then the co-efficient of QD is: