Question

The table below shows the salaries of 280 persons :
$\begin{array}{cc}\text{Salary(In thousand Rs.)}& \text{No. of Persons}\\ 5-10& 49\\ 10-15& 133\\ 15-20& 63\\ 20-25& 15\\ 25-30& 6\\ 30-35& 7\\ 35-40& 4\\ 40-45& 2\\ 45-50& 1\end{array}$
Calculate the median salary of the data.

Answer 1

$\begin{array}{ccc}\text{Salary(In thousand Rs.)}& \text{No. of Persons}& \text{Cumulative}\\ & & \text{frequency(c.f.)}\\ 5-10& 49& \left(49\right)\\ l\left(10\right)-15& \left(133\right)f& 182\\ 15-20& 63& 245\\ 20-25& 15& 260\\ 25-30& 6& 266\\ 30-35& 7& 273\\ 35-40& 4& 277\\ 40-45& 2& 279\\ 45-50& 1& 280\\ \text{Total}& 280& \end{array}$

$\frac{N}{2}=\frac{280}{2}=140$
The cumulative frequency just greater than 180 is 182.
$\therefore$ Median class is 10 - 15.
$\Rightarrow t=10,h=5,N=280,c.f.=49andf=133$
Median =$l+\left(\frac{\frac{N}{2}-c.f}{f}\right)\times h$
$=10+(\frac{140-49}{133}\times 5)$
$=10+\frac{91\times 5}{133}$
$=10+\frac{455}{133}$
$=10+3.42$
$=13.42$