Question

Answer the following questions in detail−

From the following data of pocket money given to the students, calculate Q₁, Q₂ and Q₃

50, 40, 60, 90, 80, 70, 100, 140, 130, 120, 110

Answer 1

First the given data is arranged in ascending order as follows:

40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140

The three quartiles can be calculated in the following manner:

$$\begin{gathered} \mathrm{N}=11 \\ {Q}_1={\left(\frac{\mathrm{N}+1}{4}\right)}^{\mathrm{th}}\mathrm{observation} \\ ={\left(\frac{11+1}{4}\right)}^{\mathrm{th}}{3}^{\mathrm{rd}}\mathrm{observation} \\ {Q}_1=60 \end{gathered}$$
$$\begin{gathered} Q_2=2{\left(\frac{\mathrm{N}+1}{4}\right)}^{\mathrm{th}}\mathrm{observation} \\ =2\times \left(\frac{11+1}{4}\right) \\ =6^{\mathrm{th}}\mathrm{observation} \\ =90 \end{gathered}$$
$$\begin{gathered} Q_3=3\times {\left(\frac{\mathrm{N}+1}{4}\right)}^{\mathrm{th}}\mathrm{observation} \\ =3\times {\left(\frac{11+1}{4}\right)}^{\mathrm{th}} \\ =9^{\mathrm{th}}\mathrm{observation} \\ =120 \end{gathered}$$