Question

Coefficient of quartile deviation is 1/4 then Q3/Q1 is

Answer 1

Q₃ / Q₁  = 5/3 if Coefficient of quartile deviation is 1/4

Step-by-step explanation:

coefficient of quartile deviation   =  (Q₃ - Q₁)/(Q₃ + Q₁)

Coefficient of quartile deviation is 1/4

=>  (Q₃ - Q₁)/(Q₃ + Q₁)  = 1/4

=> 4  (Q₃ - Q₁) = (Q₃ + Q₁)

=> 4 Q₃ - 4Q₁  = Q₃ + Q₁

=> 3 Q₃ = 5Q₁

=> Q₃ / Q₁  = 5/3

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

DEFINITION TO BE IMPLEMENTED

QUARTILES :

Quartiles are those values which divide the frequency into four equal parts, when the values are arranged in ascending order of magnitude.

The lower quartile is mid-way between the lower extreme and median.

The upper quartile is mid-way between the median and upper extreme

$\sf{ \: The \: lower \: quartile \: is \: denoted \: by \: \: Q_1\: }$

$\sf{ \: The \: upper \: quartile \: is \: denoted \: by \: \: Q_3\: }$

The difference between upper and lower quartiles is called inter - quartile range

COEFFICIENT OF QUARTILE DEVIATION

A relative measure of dispersion based on the quartile deviation is called the coefficient of quartile deviation

FORMULA FOR COEFFICIENT OF QUARTILE DEVIATION

The coefficient of quartile deviation is

$= \displaystyle \: \sf{\frac{Q_3 - Q_1}{Q_3 + Q_1} }$

GIVEN

$\displaystyle \: \sf{The \: coefficient \: of \: quartile \: deviation \: is \: \frac{1}{4} }$

TO DETERMINE

$\displaystyle \: \sf{\frac{Q_3 }{ Q_1} }$

CALCULATION

$\displaystyle \: \sf{\frac{Q_3 - Q_1}{Q_3 + Q_1} } = \frac{1}{4}$

By the Componendo - Dividendo rule

$\displaystyle \: \sf{\frac{2Q_3 }{2 Q_1} } = \frac{4 + 1}{4 - 1}$

$\implies \: \displaystyle \: \sf{\frac{Q_3 }{ Q_1} } = \frac{5}{3}$

RESULT

The required answer is

$\boxed{ \: \displaystyle \: \sf{\frac{Q_3 }{ Q_1} } = \frac{5}{3 } \: \: }$

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