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If Q(1)=153, P(75)=155, then coefficient...

If `Q_(1)=153`, `P_(75)=155`, then coefficient of quartile devision is

A

`2`

B

`1`

C

`154`

D

`(1)/(154)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the coefficient of quartile deviation using the given values of \( Q_1 \) and \( P_{75} \), we can follow these steps: ### Step 1: Understand the Definitions - \( Q_1 \) (First Quartile) is given as 153. - \( P_{75} \) (75th Percentile) is equivalent to \( Q_3 \) (Third Quartile) and is given as 155. ### Step 2: Write the Formula for Coefficient of Quartile Deviation The formula for the coefficient of quartile deviation (CQD) is: \[ CQD = \frac{Q_3 - Q_1}{Q_3 + Q_1} \] ### Step 3: Substitute the Values into the Formula Now, we substitute the values of \( Q_1 \) and \( Q_3 \) into the formula: \[ CQD = \frac{155 - 153}{155 + 153} \] ### Step 4: Perform the Calculations 1. Calculate \( Q_3 - Q_1 \): \[ 155 - 153 = 2 \] 2. Calculate \( Q_3 + Q_1 \): \[ 155 + 153 = 308 \] 3. Now substitute these results back into the formula: \[ CQD = \frac{2}{308} \] ### Step 5: Simplify the Fraction To simplify \( \frac{2}{308} \): \[ CQD = \frac{1}{154} \] ### Final Answer Thus, the coefficient of quartile deviation is: \[ \boxed{\frac{1}{154}} \] ---
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