If the first quartile is 56, and the third quartile is 77, then the co-efficient of quartile deviation is

Option b: 15.79. Solution: We are given: - First quartile: Q1 = 56 - Third quartile: Q3 = 77 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 - 56/77 + 56 x 100 = 21/133 x 100 approx 15.79% Hence, Option B is the correct answer.

Central Tendency & DispersionMTP June 2023 Series IQuestion 3257 of 473

All Questions

If the first quartile is $\displaystyle 56$ , and the third quartile is $\displaystyle 77$ , then the co-efficient of quartile deviation is

Options

\displaystyle 18.09

\displaystyle 15.79

\displaystyle 63.8

\displaystyle 56.71

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Correct Answer

✅ Option b — $\displaystyle 15.79$

All Options:

A $\displaystyle 18.09$
B $\displaystyle 15.79$
C $\displaystyle 63.8$
D $\displaystyle 56.71$

Detailed Solution & Explanation

We are given: - First quartile:

\displaystyle Q_1 = 56

- Third quartile:

\displaystyle Q_3 = 77

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 - 56}{77 + 56} \times 100 = \frac{21}{133} \times 100 \approx 15.79\%

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

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If the first quartile is 56\displaystyle 5656, and the third quartile is 77\displaystyle 7777, then the co-efficient of quartile deviation is