Question

Calculate $Q_1$ and $Q_3$ from the following table :

$\begin{array}{ccccccc}\text{Wages (Rs)}& 0-5& 5-10& 10-15& 15-20& 20-25& 25-30\\ \text{No. of Workers}& 4& 6& 3& 8& 12& 7\end{array}$

Answer 1

$\frac{N}{4}=\frac{40}{4}=10th\text{item}$, Lower Quartile Class 5 - 10

$Q_1=l_1+\frac{\frac{N}{4}-c.f.}{f}\times i=5+\frac{10-4}{6}\times 5=10$

Also, $\frac{3}{4}N=\frac{3}{4}\times 40=30th\text{item}$, Upper Quartile Class 20 - 25

$Q_3=l_1+\frac{\frac{3}{4}N-c.f}{f}\times i=20+\frac{30-21}{12}\times 5=20+\frac{45}{12}=23.75$