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If Q(1) = 20, Q(3) = 48, then coefficien...

If `Q_(1) = 20, Q_(3) = 48`, then coefficient of quartile deviation is :

A

28

B

68

C

`(7)/(17)`

D

`(6)/(17)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the coefficient of quartile deviation given \( Q_1 = 20 \) and \( Q_3 = 48 \), we can follow these steps: ### Step 1: Understand the formula for the coefficient of quartile deviation. The coefficient of quartile deviation (CQD) is calculated using the formula: \[ CQD = \frac{Q_3 - Q_1}{Q_3 + Q_1} \] ### Step 2: Substitute the values of \( Q_1 \) and \( Q_3 \) into the formula. Given: - \( Q_1 = 20 \) - \( Q_3 = 48 \) Substituting these values into the formula: \[ CQD = \frac{48 - 20}{48 + 20} \] ### Step 3: Perform the subtraction in the numerator and the addition in the denominator. Calculating the numerator: \[ 48 - 20 = 28 \] Calculating the denominator: \[ 48 + 20 = 68 \] So, we have: \[ CQD = \frac{28}{68} \] ### Step 4: Simplify the fraction. To simplify \( \frac{28}{68} \): - Both the numerator and denominator can be divided by 4. \[ \frac{28 \div 4}{68 \div 4} = \frac{7}{17} \] ### Step 5: State the final result. Thus, the coefficient of quartile deviation is: \[ \frac{7}{17} \]
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