Question

Q5.​If the quartile coefficient of skewness is -0.36, the first quartile is 8.6 and the median is 12.3. calculate the quartile deviation.

Answer 1

Answer:

Step-by-step explanation:

.​If the quartile coefficient of skewness is -0.36, the first quartile is 8.6 and the median is 12.3. calculate the quartile deviation.

Answer 2

Answer:

The quartile deviation is 2.72.

Step-by-step explanation:

Given the quartile coefficient of skewness $S_B= -0.36$

The first quartile, $Q_1=8.6$

Median = 12.3

• Quartile deviation measures the deviation of the central tendency of the data.
• Skewness describes the lack of symmetry in the data distribution.
• The relation between the quartiles and the skewness is given by the Bowley's formulations of skewness.

The quartile coefficient of skewness also known as Bowley's coefficient of skewness, $S_B$ is given by

$S_B=\dfrac{Q_3+Q_1-2Median}{Q_3+Q_1}$

Substituting the given values,

$-0.36=\dfrac{Q_3+8.6-2\times 12.3}{Q_3-8.6}$

$\implies -0.36=\dfrac{Q_3+8.6-24.6}{Q_3-8.6}$

$\implies -0.36\big(Q_3-8.6\big)=Q_3-16$

$\implies -0.36Q_3-\big(-0.36\big)8.6\big=Q_3-16$

$\implies Q_3+0.36Q_3=3.096+16$

$\implies 1.36Q_3=19.096$

$\implies Q_3=\dfrac{19.096}{1.36} =14.04$

The Quartile Deviation is given by half of the difference between the upper and lower quartile.

$Q.D=\dfrac{Q_3-Q_1}{2}$

Substituting the values of $Q_3~\&~Q_1$  

$Q.D=\dfrac{14.04-8.6}{2}=\dfrac{5.44}{2}=2.72$

Hence, the quartile deviation is 2.72.