If each observation in a data set for number of employees in different divisions is doubled then the coefficient of quartile deviation:

The correct answer is that it remains same.

Key Points 

 The formulae we need for solving the problem are as follows:

\(\mathbf{\text{Quartile formula for Q1,grouped data}}=Q_{1}=I_{1}+\frac{(N/4)-c}{f}*(I_{2}-I_{1})\\\mathbf{\text{Quartile formula for Q3,grouped data}}=Q_{3}=I_{1}+\frac{3*(N/4)-c}{f}*(I_{2}-I_{1})\\ \mathbf{\text{Coefficient of quartile deviation}}=\frac{Q_{3}-Q_{1}}{Q_{3}+Q_{1}} \)

Here, since all the observations are doubled the value for Quartiles becomes:

\(\text{Quartile formula for Q1,grouped data}=Q_{1}=I_{1}+\frac{(2N/4)-2c}{2f}*(I_{2}-I_{1})\\\implies\text{Quartile formula for Q1,grouped data}=Q_{1}=I_{1}+\frac{(N/4)-c}{f}*(I_{2}-I_{1})\\\text{Quartile formula for Q3,grouped data}=Q_{3}=I_{1}+\frac{3*(2N/4)-2c}{2f}*(I_{2}-I_{1})\\\implies\text{Quartile formula for Q3,grouped data}=Q_{3}=I_{1}+\frac{3*(N/4)-c}{f}*(I_{2}-I_{1})\\ \text{Coefficient of quartile deviation}=\frac{Q_{3}-Q_{1}}{Q_{3}+Q_{1}} \)

This is the same value as the coefficient of quartile deviation when the values of the observation of the data set were unchanged.

Thus the correct answer is- If each observation in a data set for the number of employees in different divisions is doubled then the coefficient of quartile deviation remains same.

Additional Information

•  The formula in this case used is for grouped data as the question specifically says observation of different employees for different departments.
• The same result can be derived for ungrouped data as well.