Discussion

The upper quartile of the data is 7.75 and coefficient of quartile deviation 0.55. The interquartile range is :

Answer: C

The interquartile range is 5.50.

The coefficient of quartile deviation is \(\frac{Q_{3} - Q_{1}}{Q_{3} + Q_{1}}\). With \(Q_{3} = 7.75\):

\[ \begin{aligned} 7.75 - Q_{1} &= 0.55(7.75 + Q_{1}) \\ 0.45 \times 7.75 &= 1.55\, Q_{1} \\ Q_{1} &= 2.25 \end{aligned} \]

So the interquartile range is \(Q_{3} - Q_{1} = 7.75 - 2.25 = 5.50\), and the quartile deviation (half of it) is 2.75.

Check: \(\frac{5.5}{10} = 0.55\). The other values do not satisfy this ratio.

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